Hello and welcome to Newsclick. Today we're going to discuss the vaccine trials that are underway and how positive or how long do we have to wait for a vaccine. Both these questions are really yours because the immune system is what your specialist is doing. So this is really up your alley. Though of course a lot of things else are also up your alley. Now the vaccine trials are on and while we have heard a lot about the modern trials we don't seem to have heard as much about the other trials underway. So can you give us a brief background of the trials and which phase we are at the moment on. Some seem to have also entered the human trials. So this is in a sense let me make a splashy statement. For the first time in human history we are simultaneously making vaccines by the oldest and by the newest possible methodologies all at the same time. So what is the oldest possible methodology? The old smallpox variation followed by Jenner's cowpox vaccination followed by Pasteur's vaccines for a variety of microbial infections. And the simple argument there was take the microbe that is causing the disease weaken it or kill it so that it's safe to be injected but it will still generate an immune response and then inject it get an immune response hope that the immune response is protective hope that the immune response is long lasting and you have a vaccine and either you are famous or you're rich. So that's the old model. Are we doing that for SARS-CoV-2 and COVID-19? Yes we are. There are at least two or three companies and organizations making that kind of a vaccine by just growing the virus killing it or attenuating it and injecting it and Sinovac Chinese company is making that vaccine and is apparently in early phase trials. So that's one end. The second way of making a vaccine is to take components of the virus particularly components against which the immune response is likely to be protected that is the outer coat proteins of the virus. So you can make the outer coat protein in a variety of ways. You can mix it with adjuvant. Everybody will remember having taken tetanus toxoid shots and for those of us who've been brave enough to actually look at the syringe the fluid in the syringe is milky and it's milky because there's a little bit of adjuvant alum mixed with alum suspension in which it is so it's a suspension. So basically you take the viral protein that you've made in a variety of ways put it with an adjuvant like alum inject that and again hope that you get protective long-lasting antibodies and I'm going to keep harping on this protective and long-lasting as we go along. There's a very large group of many many many vaccine makers in very very many countries who are trying basically to take the spike protein of the SARS-CoV-2 virus to put it with adjuvant to formulate it with adjuvant as a vaccine injected and make a vaccine and again at least a couple of those are in early phase. So this we called also as a DNA vaccines. We haven't gotten to the DNA vaccine. We haven't gotten to the DNA or RNA vaccines. No no no. So these are the oldest and the second oldest modality of making vaccines and we are doing both of those for SARS-CoV-2. The third modality of making a vaccine is actually not to put in pre-made viral protein material which is going to serve as the target for the immune response. Instead what you do through the vaccine is to give your own body the genetic information based on which your own body will make the viral proteins in a micro environment where in the body wherever you inject it so that an immune response can be generated. So rather than the first two approaches this category of approaches are approaches where you don't give the viral target to the body as a vaccine. You give the information to the body and let the body make the target and respond to the target and in this category so this is the new 21st century category of vaccine design. There is currently as far as I know no licensed vaccine made by any of these categories. It's that new and in a sense unproven category or at least. I think developed it for Ebola but it really didn't go. Well it's been developed for a very large number but yeah it's been developed for Ebola but it's never been properly deployed in any scale and there are three subcategories to this general category depending on how you give the information to the body of the vaccinee for making the viral protein. So one is you put the information for the SARS-CoV-2 protein making into another virus which is relatively safe and these are adenoviruses or adenolike viruses and you inject that virus. So what is currently in the news currently meaning over the last 72 hours in the news as the so-called Oxford vaccine is the vaccine that is based on a chimpanzee adenovirus into which information for the SARS-CoV-2 coat protein has been put in and therefore when this engineered adenovirus is put into the vaccinee the vaccinee's body will take the information and will make the SARS-CoV-2 protein and will generate an immune response against it. The second category is that also apart from the Oxford virus one of the ones which are being under in clinical trials at the moment is also a Chinese vaccine. In fact none of the examples that I'm using are unique to any one group. So multiple people are growing the virus, multiple people are making the viral protein, multiple people are making all sorts of adenoviruses mostly adenoviruses of different kinds carrying the information and the fourth category is and the CanSino group both of these were actually one of the early enlistments WHO for the clinical trials. That's correct. So the fourth group category is of DNA vaccines where again instead of putting the genetic information for viral protein making into a into another carrier virus you simply take the DNA appropriately configured and you inject the DNA and if you've done your formulation correctly that DNA is used again by the vaccinee's body to make the viral protein and to make generator immune response against it. And the last category which is exemplified by Moderna is since DNA is converted into RNA is copied into RNA and then RNA is copied into a protein rather than giving the viral protein information as DNA Moderna is giving the viral protein information as RNA directly and again letting the body make the viral protein and respond. So those are the categories and in each one of these categories there are a large number of people who are trying to make vaccines the world. So adenovirus RNA or DNA vaccines all these are in that sense new vaccine making have not been tested earlier? Yes as you pointed out there are a couple of examples of adenoviral vector vaccines that have come close to being deployed DNA and RNA vaccines haven't come that close but all three modalities have been under development and investigation for oh easily 25 years. Okay so in the laboratory they are not novel as a matter of fact none of these approaches is particularly novel because many of them are simply repurposed from earlier candidate vaccines that went a certain distance and then didn't go further because there didn't seem to be any demand for them and have simply been repurposed for them. They originally started with SARS as the target. SARS, Mars and Ebola but none of them lasted long enough for them to really get into full-blown clinical trials and then come out to the successful version. Well to be honest they lost capitalist value lost capitalist value and therefore did not go further and I would insist on that rather than saying that they lost societal value I don't think they lost societal value but what they did lose was what I'm in fact calling capitalist value. In fact following what exactly you have said that expecting a coronavirus pandemic after SARS and Mars this should have been funded so we are ready at least well before it hit us. So we got a 10 year more than 10 years time for preparing ourselves which you don't seem to have used. Well okay so let me do a little disagreement. Yes and no and then no my point of disagreement is because I think in fact that the actual technologies that are being deployed were in fact technologies that were developed and publicly funded might with taxpayer money in pretty much every country and the technologies were developed in the laboratory far enough that in fact we were ready technologically which is why all of these in a matter of weeks not even really too many months have come out of the laboratory and have gone into clinical trials. What we what I agree with in your statement and that what we have not prepared for is the downstream. Who will manufacture it? How will we put together sufficient accredited safe manufacturing to scale so that we deliver the vaccine to communities across the world as they need them without forcing them to pay through their noses for it. This component of a human response to a pandemic we have not learned at all and that's where we are going to arrive by the end of this year where the laboratories will have done using publicly funded resources what they are promising to do and then we will begin to fall on our faces because we have not done the economics of technology dissemination. Which is where the virus wars seem to be shaping up with Trump saying warp speed nothing to do with China we do not accept WHO's premise it should be available publicly and so on but we'll come to that a little later. So coming back to the the kind of vaccine development that you talked about and three of them are currently clinical trials and I'm sure more are but at least three have been talked about one is the Moderna vaccine one is the Sinovac vaccine and the other is Oxford vaccine. Coming to the Oxford vaccine because you talked about the last 72 hours news cycle that was also connected to Astro Genka which is a British company and also to Serum Institute in Pune they seem to have a retire. So the failure of the Oxford vaccine trials at least partial failure you think that is no longer now a candidate? No I think that it's a candidate I wouldn't call it a failure so let me clarify since you bring up the detail of the Oxford vaccine essentially the most likely expectation from pretty much all of these vaccine approaches that we talked about is that all of them will work to a certain extent meaning will they generate some degree of protective antibodies and protection? The answer I suspect will be yes and that has in fact been borne out some in the monkey experiments preclinically some in both the monkey experiments and the initial small handfuls of humans who are immunized with them that antibody responses have been generated that are that have protective properties and in the monkey experiments there is actual protection however and that's where the qualification about the Oxford vaccine appears to begin is protection a yes no phenomenon and no it's not so essentially what seems to be happening is that in the Oxford vaccine monkey experiments unless I'm misunderstanding the data there is clinical protection meaning the monkeys don't become diseased there is a virological protection partially in the sense that the lower lung load of virus is substantially lower but the viral load in the upper respiratory tract does not seem to have gone down as dramatically now what this means if it means anything at all either in terms of success or failure is quite unclear but I would think that the likelihood is that as a first generation vaccine this is going to be as as successful as the scientific vaccine or as successful as the as the Moderna vaccine or or indeed any of the other vaccines I don't think that we should be expecting too much of any of these in the what I'm calling series of first generation COVID-19 vaccines that will begin to come out by the end the Moderna and the Sinovac vaccine seems to show that the monkeys did not get infected that when they were infected later by the actual virus yes and no again it's not clear to me that the monkey experiments in the Moderna and the Sinovac vaccines were as extensive as those for the Oxford vaccine and both of those showed substantial reduction in in in virus load and so it's all you know give or take a little bit it's all comparable and they're all within the same ballpark I would think at the moment so you think that the vaccine is still very much in the race absolutely okay so the question is we have three candidates in the race who have gone to a certain distance others may have that we haven't received enough notice about them partly because they may not be as well connected to media or needing the share price boost which some of these companies seem to do so there is obviously both these angles playing here but we would say at the moment probably there are six to eight candidates which are which have started running in terms of what would be called the two class of trials that are there so both these vaccines both this these set of vaccines and a few others are doing clinical trial one and two now what's the difference between the one and two series of clinical trials yeah so um keep in mind that um all the preclinical work that we are hearing about falls into two categories before I get to the clinical trials the preclinical work is immunizing animals uh getting antibodies from them and testing to see whether they have protective properties this is universally true so there's a hundred and something vaccines registered in clinical trial registries across the world for prospective trials and I suspect that at least in two thirds of them if not more and the simple experiment of immunizing small animals with them mice rats rabbits guinea pigs and finding antibodies with protective properties have been successful so that's one the monkey experiments which is where you can actually look for protection because you can infect the monkeys with SARS-CoV-2 and look for quasi real-life protective capacity of the vaccine have been done for much smaller numbers in part because monkeys are expensive not easily available in part because monkey centers which do monkey experiments using SARS-CoV-2 are even rarer so groups are lining up and uh on a waitlist for this so those are this handful that we are talking about in the clinical trials the first stage of clinical trial is to take relatively small numbers of people certainly less than 30 usually about a dozen or so um and the formal question you are asking in a phase one clinical trial is whether the vaccine is safe or not so the primary stated um intention of the clinical trial in its first phase is simply safety not either um it's the ability of the vaccine to generate an immune response leave alone the ability of the vaccine to protect okay however since you are immunizing a few people you will take blood samples and you will test those blood samples to see whether there are antibodies and if there are antibodies what the protective characteristics of the antibodies are if there are any and it is from those very tentative preliminary results that we are hearing noises okay all over so this phase two clinical trial will be with larger numbers of people and will begin to ask questions about does the vaccine reliably generate a protective immune response i have i have as yet not formally heard that any of these trials has begun phase two although i may be behind hand on my information um i do expect that within a matter of weeks people will start phase two clinical trials and in fact as i said some of them may have started already but we have no result suddenly from phase two clinical trials is yet and it is in the phase two clinical trials that the ability of the vaccine for mutations the vaccine candidates let us call them to generate an immune response that looks protective will be tested whether the vaccine in fact protects against actual SARS-CoV-2 infection and COVID-19 disease or not will be in a yet further stage of the clinical trial and there depending on what the incidence of infection in the community is very large numbers of people may have to be recruited for those trials that's a phase three trial that's a phase three trial and it's in those situations it's with respect to those situations that people are now talking about controlled human infection models for rapidly validating the protective capacity the actual protective capacity of vaccination where you will take relatively small numbers of people vaccinate them give them deliberately give them infectious virus with appropriate safeguards and therefore ask whether the vaccine protects or doesn't protect with quick definitive results from relatively small numbers of people but with some amount of risk so that's the something which is new this is not a normal vaccine development program no the the controlled human infection model chimps as they're called has not as yet been used to license any any vaccine currently in the market all vaccines currently in the market that we have followed the conventional phase one phase two phase three trials that we talked so when you talk about the phase three trials that takes the longest time it takes the longest time for a variety of reasons large numbers of people are required for statistical reliability and you have to wait for long enough for natural infection incidents to accumulate large numbers of examples of disease in both vaccinated and placebo so it can be about three months four months six months oh i can imagine that if by then across the world transmission efficiency of COVID-19 has dropped substantially phase three may take longer than that so that's why we are talking about the controlled human infection model human infection model that's the reason yes okay so if this happens say what the United States is saying they'll have a vaccine by fall we still have the question of scaling up production we are not entering into the issue you have raised whether it will be available at a price which people can afford particularly the global community this is of course the battle which has been now just fought in the World Health Assembly as you are aware of and the United States and the UK being particularly unhappy with WHO more or less throwing its weight behind the argument and which India has also passed you to that this should be a global public good which Chinese prime minister president seems to have agreed to so do you think that this issue of scaling up production before we go to the in who controls that scaling up production particularly if it is the old-fashioned vaccine will be simpler um actually surprisingly scaling up production is easier with the what I call the newer category of vaccines the adenoviral vaccine the DNA vaccine the RNA vaccine these are paradoxically far easier to scale up in fact as you go from the newest method modalities of vaccine design to the oldest scale up becomes technically more and more and more difficult in fact that's the major reason why so many companies and organizations and groups across the world are trying to make vaccines in these relatively new unproven I suppose you could say modalities because scale up is going to be much easier if and when one of them or more and more than one existing facilities that countries have for instance a serum institute or the afghan institute they cannot produce live back live or inactivated vaccine oh in the existing scale so so none of the technologies is difficult in the sense of these biotech industrial organizations being unable to absorb the technology it's simply that the so there's a built-in limitation how much virus can you make in one liter of tissue culture is a limited so it's not so much a matter of knowing how to do it it's a matter of how many millions of liters and it's simply the physical infrastructure of scale and that's going to be for example sine of x problem sorry to interrupt something you have to build it a new it has to be built specifically for this purpose exist no it doesn't but keep in mind that if we are talking about a global demand over a very narrow window for vaccines we are going to need more doses of vaccine per month than we have ever imagined okay and it's in that scale will lead that making whole virus inactivated vaccines is going to I suspect run into scale up difficulties and that's where the RNA and the DNA might in fact be a little easier for scale up okay so what you are saying is that in that sense the advantage to scaling lies with the newer vaccine technologies so it's not very surprising efficiencies of the newer technologies tend to be higher than older technologies in a sense yes okay so if this is successful say in the human trials phase three trials and if the controlled human infection strategy works so do you think a target of say fall as the Americans say or September October is realistic right so let me say something about benchmarking and decision making I think it's entirely possible if the pandemic continues to worry the world as much as it is wearing the world currently it's I think it's entirely possible that regulatory authorities across the world will accelerate approval processes so that with evidence of immunogenicity meaning that the vaccine generates an immune and antibody response and that the antibody response in laboratory testing has protective properties that much might be eventually approved as sufficient for licensing I don't know this but it's it's at least possible beyond this there will have to be a formal clinical trial for the infection which would be the the orthodox way to go or the controlled human infection regardless do I think that by autumn fall as the Americans call it we are going to have a vaccine rather than a vaccine candidate I doubt it do I think that we will get there by say next january or so I think that by next january we will begin to see the first clear unambiguous results that multiple different vaccine candidates do detectably well in protecting so my guess is I suspect a little uncharacteristically I'm being a little optimistic but my guess still is that by early next year we will begin to see this data I doubt seriously that we are going to see the unambiguous data which allow regulatory approvals by the coming on okay and the last question if we have it by end of the year beginning of next year then parallely we could scale up production so that when it hits us that means we have this vaccine scaling up should be relatively faster so you mentioned that the serum institute of India which is one of the world's major generic vaccine suppliers has a tie-up with the Oxford vaccine development group and that tie-up in fact is an interesting one aimed precisely at what you're talking about which is preemptive scaling up and the interesting part is the preemptive part by and large you would begin partnerships of this kind you know almost franchising partnerships of this kind for scale up across the world in multiple centers when you have a vaccine that's working okay and in that sense I'm pointing out that what's interesting here is that this is a preemptive scaling up in the sense that the serum institute is investing in a speculative scale up of the Oxford vaccine at least from their from their own description that's what it sounds like yes in fact they have said that we can afford to spend the money because it's our money we don't need any approvals so the Poonawallas have said this is okay for us and as you point out they are one of the largest in the world in terms of generic manufacture AstraZeneca is an interesting case because this is why the UK government has been against the patent pool on the in the vaccines being declared as public good as much as Mr Trump so always have the flip side of public funding in terms of the Oxford vaccine is publicly funded but it then becomes privatized to AstraZeneca and then of course not available to the rest of the world yeah so that's interesting and so keep in mind that AstraZeneca wasn't born as a UK company it was a it was born unless i'm mistaken as a Scandinavian company but with with multinationals the point of origin becomes pointless after a while but but the fact of the matter is that this is not really to do with Moderna or AstraZeneca it is to do with the broader both practical and ideological commitment of how governance and major industry in western political economies are configured to be complementary to each other so the the the US and the UK governments will in fact point out that their public sector contribution of science and technology development is in fact intended for the marketplace to take advantage of so there is there is an element of the generic ideological fervor involved in in their positions as well and of course the fact of the matter is that what they will do is sufficient negotiation that their national populations will have some reasonable access built as in in return for their support of these companies in the international arena for intellectual property right protection so it's going to be a complicated dance of who's trying to get what advantage for which corner of their own and and i suspect that the straightforward position that we are spending public money across the world in trying to deal with a problem that's worldwide and that therefore we should simply all of us get together and spend whatever money is required to make the solutions available across the world that apparently common sensical point is i suspect going to get subjected to a major barrage of special interests it's interesting the salk vaccine if you remember johanna sol is a salk was asked exactly this question and he went to patent it and he said can i patent the sun so it belongs to the people the salks are no longer the ones who are there even now bat batting purified insulin and yes earlier in fact the same thing that he he sold he gave the patent to the university of toronto for one dollar and when he was asked he said it's not my insulin it's it's everybody's insulin yes that actually comes before salk so you know that there are there are different ways of looking at this yes but and that's where we are going to be those are going to be the major wars in boardrooms across the world come next year yeah and i believe satyajit that this will be a repeat of the aids wars and ultimately the fact that once you know that this works repeating it is relatively easier and therefore that compulsory licensing to other mechanisms will also come into play so i don't see that this will take 10 years which is what aids back aids drugs took before it became accessible to the poorer sections i don't think it's going to be that long but that's a hope that's you where it actually with you let me add something to what you said that may be interesting and that is you see the anti hiv anti aids drugs were being developed in relatively small numbers of laboratories primarily distributed in the development here is an extraordinary distinction that i think we in india and in fact we across let me say the global south should not lose sight of and that is we have friends and colleagues in laboratories of the global south who are making sarkov to covet 19 vaccine candidates using exactly the same methodologies and technologies that are being used in these other places there are a bunch of efforts in india for example to make vaccines by one or the other of these methodological categories that we talked about and my argument is that we need to be heavily supportive of these efforts because they underline a major tactical point so this is not about they are necessarily succeeding and making great vaccines that will go out i hope that they do but it's but my support is not dependent on that i'm arguing that we should be supportive of those because it undercuts patent claims as and when they begin to get made okay and that i think is and i'm saying this publicly is a critical issue in underlining the point that the state of art knows how to do this the world over okay and therefore we need to be both supportive of ongoing efforts and we need to demand the poorest of us as countries need to demand hey can you support some of our scientists and technologies to try to make a vaccine candidate good so the battle continues absolutely your vaccines which it did over the issue of aids and as i said hopefully it'll be much shorter and if you strategically invest in some of the issues you are saying some of the areas of research development as you are saying then we'll be in a stronger position thank you satyajit for being with us sharing your knowledge about a rather complicated issue which is of great interest to people as and when such pandemics or other such issues come up this is all the time we have a news click today do keep watching news click and do come back to our also visit our website


Now, what we are driving towards is quantization of the gauge fields, a quantization of the young mill system. And the canonical structure becomes very important because you remember that we started our course by defining the path integral using the canonical formalism. We had the canonical variables and we had the fundamental relation q p equal to we traded these two things right. q p equal to i h cross is same as saying that the q p overlap is equal to e raise to i q p over h cross and square root 2 pi h cross. So, canonical structure is very important to us for quantizing and that is why we have to be careful about what the canonical structure of these equations is. And so, towards quantization quite a lot of subtleties arise. Now, historically it turned out that this was very early days and nobody thought that young mills fields will become important. They were proposed in 1956 and throughout the 1960s people were mostly concerned about spontaneous symmetry breaking. They were trying to get pions as goals you know superconductivity of the strong force and things like that. But Feynman had begun to worry about this and there was famous quantum gravity person called DeWitt. Bryce DeWitt is a name not known much now to the to the ignorant, but to the those who know it is a big name because Bryce DeWitt gave his full force to quantize quantum gravity along the canonical method, but actually more adopting swingers he was a Schwinger student. So, more adopting Schwingers Schwinger had his own way of saying how you vary the action. So, it is a functional approach, but not path integral one and then in later life Bryce was a professor at Texas Austin and I have taken courses from him. So, Bryce DeWitt wrote a trilogy. So, he has a book called Dynamical Theory of Groups and Fields in which he meant to attack this problem of systems that have this kind of redundancy and as we know general theory of relativity has the huge redundancy due to reparameterization invariance and the covariant derivative of differential geometry. So, Bryce like a juggernaut just cleaned out the whole field of doing what was required. So, Newton was somehow interested in this in the Young and Mills proposal and he observed that from a very physical point of view that the gauge conditions shows rather that the superfluous degrees of freedom can be co-variantly removed by introducing Gauss. Gauss diagram is one that has a scalar loop it could have anything outside, but it has a scalar, but the diagram has overall minus sign. So, it has to be subtracted.  So, you say that diagrams like this have to be subtracted. So, you can interpret it by saying that well you know in Wicks theorem that when you have closed loops of fermions you get a minus sign because of the anti commuting property. So, you would have had psi psi from this vertex. So, you know how the Wicks theorem will go is that you have a mu psi bar gamma mu psi normal ordered and a mu psi well you would have a mu psi bar gamma nu psi and you have to link this psi to this psi bar and this psi bar to this psi, but in doing. So, that would give you this diagram. So, one a mu coming in reducing psi and psi bar you know one arrow going this way one and another one like this and then you have to. So, this is one vertex this is the other vertex this is the product of the two. So, you join up these lines that joining up in Wicks prescription is coupling this psi bar with this psi and this psi with this psi bar, but that will require going taking this psi across one psi bar. So, sorry this is normal ordered. So, there is no question of going across that, but it entails a negative sign from having to take the psi across to this side ok. So, then it becomes a propagator. So, that minus sign normally comes if you have the fermion statistics there, but here it is difficult to see how minus sign would come. So, people said well treat, but and it is required to be scalar there are no indices on it. So, people said well all you do is that you claim that it is a scalar, but a fermion, but it never appears in the asymptotic states. So, it is not going to violate our spin statistics theorem. Spin statistics theorem says that scalar cannot be a fermion, scalar has to be a boson all integer spin and 0 spin have to be bosons, but this violates normal that condition. However, it is not going to be seen outside it is only a trick in the diagrammatic calculation. So, that is what Feynman observed and he probably did not say it was fermionic loop he just said these need to be subtracted. Bryce Dawitt in his own juggernaut way just came to the point and say ok you need to put this and you need to put this and he never realized that he had done the same thing. But out in Lebedev Institute Russia two Russians were worrying about this and they had read Feynman's paper. So, Fadyev and Popov this name is 2 D's and 2 E's, but there is an apostrophe here. They gave a completely field theoretic interpretation, because they had a colleague called Berezin who for his own mysterious reasons because he was a Russian had already worked out how to deal with field theory of or quantum mechanics of Grassmann variables. Well I know why he had got it out. So, Berezin's observation was that if you are going to do path integral quantization of fermions, fermions have anticommuting property. So, classical limit also they must be anticommuting, but if it is so, then they cannot be ordinary numbers. So, they have to be what are called Grassmann numbers which anticommute their product is not even I mean you cannot express them as numbers and those variables have to be anticommuting. So, just around 1962-1963 he worked this out Feynman is also around 1961-62 and then Fadyev and Popov realized that what they need to say is that they use Berezin's method, but they violate spin statistics theorem then they can actually get Feynman's ghost diagrams in a systematic way from the path integral. So, that is what we are going to do next yeah. Oh I just wanted to tell the story that in America nobody was worrying about this because they were not looking at Yang-Mills field theory, but in Russia it was stronger nobody was supposed to look at field theory at all because Landau had declared in 1960 that field theory is dead QFT is dead in a major conference he said this based on his analysis of quantum electrodynamics. So, there are two problems first of all you would like to know the good news that all the perturbation theory that you have been using is wrong from mathematics point of view because it can be proved that the perturbation theory perturbation expansion you make is only asymptotically convergent or they are actually called asymptotically divergent series. So, first thing is that perturbation series is an asymptotic series they just call it asymptotic series. This means that the terms grow smaller I just draw a diagram like this. So, series goes like this keeps growing smaller, but then it begins to diverge again the terms begin to diverge again ok. Now, this somehow was already noticed by Pankare much earlier and so, he had warned people that you should cut off your calculation here while it is still converging cut it off and interpret that as the answer do not go to the bitter end of the series. So, that was one problem that anyway perturbation series people had doubts about, but Landau further showed for QED that there is Landau ghost. Now, this is a different ghost not that ghost which is an essential singularity at order 1 over alpha. So, if you do QED to 137th order then there is a essential problem. So, he said that it is not even benign like what Pankare said. So, this is Pankare's prescription, but that there is an essential singularity and therefore, this does not make sense. I am quoting this because it is important to remember in history of science that great men can be when they are wrong they are very badly wrong. So, there was of course, no reason to stop studying quantum field theory, but because Landau declared it nobody in Russia was working in quantum field theory. So, Fadiyev recalls many years later about 5 years later he has given some set of lectures I think in TIFR actually there on the video that it was like censorship. So, they secretly brought out a preprint, but did not show it to anyone and then the preprint migrated to Europe secretly in somebody's suitcase and when it reached the west everybody was enlightened and then said hey because by then it was late 60s 1967 or so that, but I think so in 4 to 7 they first wrote this in 1964 the preprint migrated out they never published it, but by late 60s young males theories as applicable to weak interaction had come back in vogue. So, it was Ben Lee I think B. W. Lee one of the pioneers of perturbation theory for spontaneously broken electromagnetic theory he brought it out as a Fermilab preprint. He reprint he translated and produced it as a Fermilab preprint and after that by 1967 they actually published it as a physics letters paper in the typical Russian style where each page is like 50 pages of calculation. So, they just wrote up the note their whole lecture notes they wrote in 4 pages and that appeared as physics letters been 1967 and I think David's book up is actually this books date is also 1967, but he had already a set of papers in physical review 3 papers. So, it is called the trilogy. To all the older quantum gravity people up to year 2000 David's trilogy was the Bible of why quantum gravity does not work or if you had to do it how you would do it and it is very useful document because if you actually do calculate he has done all the calculation which you cannot imagine doing. Now therefore, this Padya and Popov came out with a very elegant way of doing things they were of course, in this mold of Dirac. So, they said that corresponding to a gauge constraint you also put gauge conditions on the phase space and we write like this because this is a this is a formal equality it is not a not really a function it is some expression on the space of q's and p's which is set to 0. And so, introduce sorry I am sorry that is the second line. So, constraint the first line is constraints that is our these things ok. So, we already wrote C for it. So, we have constraints C. So, we introduce gauge conditions this nomenclature also has lot of disputes, but it has stayed. So, I will not bore you with that. So, we introduce gauge conditions gamma a such that they are complementary to this C they choose a particular point out of this. So, the problem with this C is that if you draw some n dimensional phase space ok. So, let us say q q i and then p i lots of dimensions and you have a constraint surface right in this big space you have you are supposed to be restricted to that and the point is that if you actually try to do path integral and kept cutting it at lot of places you are doing redundant integration.  So, the gauge condition gamma are supposed to be something that cut them in a judicious way. So, gamma should fix a particular trajectory out of it for the timing I will draw I mean I do not know how to draw it, but so it will choose a particular point out of these. So, that you are not taking care you are not integrating over superfluous degree sorry I am sorry one moment. So, the fact that C equal. So, superfluous integration would happen perpendicular to it because C equal to 0 is the physical surface. So, you would be integrating within that and going outside of it is actually not required. So, you want to fix it so that you make a particular choice of unique variables out of the constrained ones and that is done by erecting a complementary surface gamma. Only thing is I do not want any overlap at all I just want one point out of it right. So, the correct thing to show would be to draw a stack of these 0 1 I mean any number any fixed number would be fine. Any one of those is a valid surface and you want to select one out of it that is the correct thing to show which is a little hard to draw ok. So, it is equal to some alpha i at some constants. So, any one of them is fine because if you set it equal to some constant it is ok. So, you put this gauge conditions which make a choice out of this stack of surfaces and an example is we know take Maxwell we know the equation 0 or some constant or some external current . This reads box of a nu right d mu d mu a nu and minus d nu of so, exchanging order of these. So, Lorentz not Lorentz observes that if you set d mu a mu to 0 then we get only box a nu equal to 0 which are just the allumbarsian independent equations for each variable. So, this it is no longer tied up with derivatives of the other components and they become all free ok. So, this is the gauge this is our gauge condition gamma or gamma a ok the condition is this of course, that also does not fix everything because as we know there are two different things. So, in this if you now set a 0 to be trivially 0 then you will get that divergence a would have to be 0 which is that a has to be purely a curl like field, but this is the meaning of putting this. Now, in the canonical language we can then think of the gammas as some kind of conjugates to the gauge conditions. So, there is a ancient book called Hansen, Raji and Tytelbein. So, I am going to explain a few things out of that book. This is a very arcane book, but somebody has brought out a new version now we were taught by Tytelbein. So, and Tytelbein has now a new name he is called Boonster. Tytelbein is a very clever Chilean physicist. He was working on quantum gravity according to Bryce David program, but using functional methods path integral methods and John Wheeler thought that he was going to crack the problem of quantum gravity. Anyway Tytelbein went back from Texas to Chile and started a new institute and then later he changed his name to Boonster. Whatever that is coming back to this the philosophy can be stated like this that we yes here. So, the philosophy is that identify CA with the with new configuration space variables, new coordinates, some subset right. So, from Q i you switch to C 1, C 2, C j and then Q star 1, 2, 3 the starred one will be free. So, you somehow do this transformation on the phase space and then you try to so, yeah then you try to treat the gammas. Gammas themselves will not be conjugate to the C, but you arrange it so that you find conjugate. So, then solve for P i in. So, now you claim that so, your gamma a were on the phase space. So, they were functions of Q i and P i. This can be written as gamma a of Q i of you know the Q tilde. So, C Q star P i of sorry C Q star and P P star. So, you make a this is all formal nobody is telling you that you can actually do it. The claim is that if you can first you adopt some coordinate transformation such that the ones that are unencumbered are grouped as Q star and the ones that have any problem with them you just put the C 1 to j whatever constraints you have treat them as coordinates on this phase space now. So, it is a non-trivial statement. So, actually not so, I should say coordinates on the phase space. Then formally propose that P 1, P 2, P n similarly becomes that I should have written. So, where can we write it?  So, you list them and put here some symbols P. Now, you substitute this over here of course, what to substitute you do not know. So, you are going to just write them as functions of Q to begin with, but let me just write out the formal procedure then you can think about what is actually doable and what is a merely a statement of existence of such transformations, but the point is it conceptually clarifies to us what is going on. So, if you do this wherever in the old phase space you replace all the small Q and P by the condition C and the unencumbered Q stars some formal P's and P stars and similarly old P's like this and that said that is equal to 0 there will be as many of them as there are this fictitious P's. So, you solve these to find P's in terms of gamma. So, you invert this to determine the capital P in terms of the old Q and P. So, you solve for capital P in terms of Q star P star C that solve that is really because you are going to invert it and C's are anyway equal to 0. So, but you will have some formal expression for the capital P in terms of Q star P star and the C's and now you. So, in order for this inversion to be possible it is necessary that the gamma and the old P are conjugate to each and the P's are conjugate to each other the new P's. So, we need that. So, we are coming to somewhat crucial condition that comes out of all this rather formal mumbo jumbo which is that very. So, the formal statement is that this set of equations should not be equal to 0, but this we can now cleverly state as right we need this because we are going to to find this solution you need to there has to be independence of the variables gamma and there have to be as many gammas as P's and they cannot be coinciding with each other. Otherwise you will have a 0 in the if there is any 0 in the determinant then you will not be able to invert. So, you require this, but then you look at it and that is note that this is nothing, but the Poisson bracket of gamma A with the C's because there are as many capital P's as gamma. So, temporarily use that index, but that is same as saying that the determinant of gamma A C B should not be equal to 0. This is the real requirement on gammas. So, now you see that you do not have to worry about this fictitious P's after all, but this is how one thinks to arrive at that answer and we can see that this C and this gamma will have a nonzero commutator the Poisson bracket. So, you can do it, it is actually visible trivially, but anyway you can do it. So, because there is no A 0 in this and the only dot there is A 0, other things are all canonical, sorry I am going to reverse one minute. So, what we mean is the A's and pi's of course, pi i with A i will have non-trivial Poisson bracket delta 3 of xx prime. They are of course, functions of space, but that you do not x prime and at a fixed time we do this here. So, you will find that there are non-trivial Poisson brackets left over and then it is not collapsing to 0. So, that selects for you the physical phase space. Now, next time we will complete the Fadiya Popov trick where we will see that this determinant is what is going to be an important feature, not that determinant itself after one more reinterpretation of that determinant it will enter in the final answer. So, we will stop today.


Welcome to Toffy TV, it is the match preview, Everton vs Norwich City, 3 o'clock Saturday afternoon, Goodersham Park, Anthony Taylor the referee. There you go, our friend from VAR last time out against Spars. No friend of ours. And during the day, Andy. Andy, game that represents an opportunity for Everton to get back to back victories for the first time this season. Obviously Norwich City turned off a goodersham bottom of the league, decent football inside, but not in great form, so a good opportunity for us at the weekend. Yeah, obviously we can't take it too lightly and we can't make any assumptions, but you look at the fiction, what Norwich have done so far this season. You think to yourself, Everton, even at 80% of the best, should be able to get the result. But you want to see good Everton performance really, you want to see a couple of goals and see what's put the game to bed early. You want to see put Norwich under pressure because when teams are down at the bottom, you can't give them little windows of opportunity in games. I think they need to stamp their authority early in the game. Picking the right sides is going to be important and same as you're trying to, they're not going to be a team that's going to sit behind the ball as you play flow and attack on football, have pooch here on the counter. Do you might have a chance or two on the counter? Hopefully not. But we need to put the game to bed early, get a goal early and get the fans behind us. As Pad said on the podcast, the fans shouldn't come with an air of expectation. We need to get behind and make a good atmosphere if you will and put pressure on a team that has struggled really. Los nine out of the opening 12 games, only one two, one of them was an absolutely brilliant victory against Manchester City. We played, even though City dominated that game, at times Norwich played some great football and beat City's press quite a few times, with some lovely pass on football and took the goals really well, Pookie outstanding. So they got that in the locker to play that way. They were brilliant in the championship last season, absolutely fantastic. We've got some really good players. Wendy is a player I watched in the championship last season. He's a really good creator, gets between the lines, can receive it in tight areas and create for his team. Pookie is a one-touch finisher, a really good player to get a chance to put away. If you look at the stats this season, he scored chances that he wouldn't expect to have scored, XG if you will. He's put a chance away, so he's taken his opportunity as well. It's up to me to snog it and get him in. I've come on the last couple of weeks as a partnership then, hopefully we'll be able to snuff them out. Dems there, I'd say would be the two danger. Steeperman is a pretty good player on Al-Hinanda. I like Todd Cantwell as well. He plays also in the Takhamer field area. It's defensively they've got the problems. They've got two really good young fullbacks in Jamal Lewis and Max Arans who haven't fans of head, haven't linked with him before. Good young fullbacks who get up and down. But then you've got Ben Godfrey who's played defensively a field before. He's still finding his way. He's similar to John Stones when he was quite young. He's that type of centre off. I haven't really got a centre off next to him who's quite commander enough. He could lead them through a season. They are quite open at the back. Hopefully, with Charles, I think he can score 15, 16, 17, 18 this season. I think it's an opportunity for him. Hopefully he will be plays. I wouldn't rush bin our back, but hopefully he's fit to play. If he is fit to play, I'd like to see him play as well. Hopefully we'll go with our best attacking options and put the game to bed early. You've got Tim Krull in goal. He's a good goalkeeper for me. He likes a good game against Devon. He's put some good performances in. We do have to be wary of him. I do like Max Arans. He's been linked with Devon a couple of times. I think he's a player who we'll keep an eye on because he does like to get forward as well. From our perspective, it'll be the battle of the 4-3-1s. Probably, a lot of Evertonians want to see us playing 4-3-3. They showed last season, 4-3-1. I know people will be bored of Everton because of how stale it's got. But there is a way to play it when it is exciting. There is a lot of movement. I showed last season the championship. I'm not going to be able to show as much this season. But if you've got the right person now, and I think you saw it against West Down, when we did have the right person now in terms of fluid front three, a will be spraying passes in and you've got Sadibi in the side now as well. I think it's coming together. The formation, we'd all like to see maybe a 4-3-3 and maybe get more players in the field area, have people breaking from the field. But it's also working itself out at the moment.  Hopefully, because he came on, he was good against Southampton. Hopefully, he's back in. The formation's not really... I think it's still an issue in a sense. But I think it's with the right players. We can be our best, really, in a formation. Well, he scored this week for Nigeria. He did, yeah. And had an assist as well. He was captain, actually. For Southampton? Yeah, done. And the opportunity there for confidence-building came on against Southampton, like you say, and played the ball that we eventually saw from from Sadibi and done quite well. So, maybe the manager will go for him in the middle of Lo Guilfee, scored for Iceland and missed the penalty as well. And we've had... Cheng's team. We've had... Pucki, who scored for Finland as well as they qualified for the Euro. So, you know, players in this game who've done well for the country while they've been away in international duty. But I think just from our perspective, you know, obviously, the opening 12 games haven't gone the way we would have liked. But we won last time out, which was a big thing going into that international break with an away win. Got that, you know, that out the way because it was dragging on far too long.  You know, that's how tight the league is. So, you know, if we can get these three points and be on 17 points on Saturday night, you know, that'll be a big thing, I think, for confidence-wise. It'll make them feel better about themselves. It puts a big gap between the bottom three, four teams and we can start looking up then. We're going into a very difficult period. We know all about that. But I think if Everton can go to Leicester with back-to-back wins in the Premier League, they feel better about themselves. And, you know, Leicester have got a tricky away game at Crystal Palace. I don't know about the tricky game this weekend anyway, as well themselves. So, we'll be going into that game if we can win this thing, we can get something from that. But that only works if we do our job. Now, not a genre team that's going to come down low, but I shouldn't imagine, because they haven't really done it this season. So, they're going to play open football and try and catch us. Set pieces, we've got to be worthy. They've got some tall players and Everton, you know, 50% of the goals we can see that almost have been for them. We don't allow many open-play shots. We haven't played many of the top teams yet. So, that's slightly skewed. But even so, we do separate. We are good at spreading shots. We have got a really good press, obviously, and Mason Allgate has done well on recent weeks. So, yeah, you know, we just got to live at their chances, really, obviously, as I said, Pukie can score from, you know, different types of goals from different angles. Just got to keep on up the game, really, and not get caught on the breakers, I think. It's going to be a game where we are committing them forward.  And I think, you know, I don't really want to say expect this to him, but I sort of do, because I think this is a perfect game for Everton. I think a West Ham is going to be quite open for us, and, you know, if we can put them under pressure, and they don't obviously play through us in any way, then we will win the ball back home. We should create opportunities for ourselves, so... Listen, if you're not... if you're not confident about this game as an Evertonian, then I said, yes, there's probably not going to be many games you're confident about this game. No, I think we are, and I am, but it's... No, we're not talking about you, but just me and Evertonian. No, I think Everton play should be, because you know what the Premier League is like.  I mean, Norwich have lost 18 at the last 21 of Premier League away games, so we haven't travelled brilliantly. Obviously, Norwich away is always a tough game, because Carrow Road, for Everton especially, isn't great, you know. Are we good at any ground? Up to par. I mean, the property is that. West Ham away is not that bad. You know, when you look at it like that, but Norwich have kept a joint league one Premier League clean sheet this season, because basically they are open. They've come off playing the same way, and you have to take your hat off to them that they haven't tried to... They've still tried to go with the principles, and I think... It works for 1700, doesn't it? I think you've got to look... The basic for them is, due to web is the spot on direct, and I listened to an interview for them from this summer, and he basically said that they can't really afford to change the range, because a lot of players have got a bonus kickers where they went up a wage when they went to the Premier League, and by keeping those players, because obviously they expect to also get relegated this season, they weren't going to take on a load of players on Premier League wages, which they would have had to get rid of. So there's a talent gap, and I think they've got some really good young players, and they found some really good bargains in Wendy and Pukie last season, and I think they expect to go down. He even said that he's two years ahead of the plan from where they expected to be, because Daniel Fark in that first season didn't do great, and in the second season he surprised everyone, won the title, and I think they'll go down this season, but I don't think that's not part of the plan. I think they'd love to stay up, obviously, but I think they didn't take on all those players like Aston Villa who obviously don't make or break whether they stay up or they need to stay up, because they took on so many players, and they were Sheffield United. I think they'll probably stay up, but they didn't spend a load of money to try and compete in the Premier League, and that's the difference. I think they're built to go back down. If you look at Burnley, when Burnley came up, Dych didn't spend a lot of money the first time around, they got relegated, and he bounced back up, because they only bought championship players when they were in the Premier League. So the set-up's good to be a yo-yo club, really. I think Daniel Fark is a decent manager, and he'll go out as far as to say he should be managing time. Some people talk more about the Man City game for bigger jobs, and he's a good coach, but I think he should probably stay at Norwich. Playing the principles is good, and I think sometimes you need to skew them a tiny bit against City. They did have to sit back, because obviously Man City came up with so much pressure, and they did spring on the counter-attack, but I don't think they'll play like that against Devon. I think they'll play relatively and that'll leave gaps for us to exploit, and they'll have to take the chances in this game, and early, because the longer games go on, we don't score, then you know, the more... I mean, make a day a look at it as a game, you can win, because, you know, we're not in amazing form, we're quite strong and good at it.  That's what I mean, that's the problem with me there, yeah. I'm confident for Saturday, of course I am, and I think the way they play makes me a bit more confident. I think we can beat anyone at home, and we generally do. We have got a very strong home record, but we'll have to be on our game. The minus 17 in the goals, so obviously it's yesterday, that open... Yeah, one goal, salt, and something like that, the 9, 0, so excuse that. But you're talking about Aston Villa there, and Aston Villa spent under 35 million or something in the summer. And they're off four points above Norwich. It takes time to knit a team together again. No, but I'm saying... So you're looking at the two sides of it there, aren't you? They play a similar way, they're fairly open as well. Aston Villa, I think might just stay up, because they've got a bit more quality about them, but you never know. Villa beat Norwich heavily at Carroll Road, didn't he, 5-1 or 5-2? Villa go with... We'll obviously get a bit away from Norwich, but when Jack Grealish plays, Villa tend to do better, because I think the record with them without Grealish is vastly different sometimes. But yeah, there's some good players on show on Saturday for Norwich in terms of... I like the follow-backs. Obviously my errands gets more the depressed, but it was a really good young left back. Ben Goffrey, as I say, he wants to watch, but he needs to learn a bit more. He needs to get his position and so on. Much like Holgate, really. Holgate's probably the under-reaster part of this game. He's on the ball, he's got two assistants, last three games, isn't he? So I think that he's added that bit of an element to pass off on the back, because he's not great in terms of on the ball. But from centre back, he looks much more assured and he can drag it into midfield, and that gives us a different element, Ben, because if he can carry it into midfield, then he causes someone to come out of the... It'll be a medium block for Norwich. For a medium block to come and cover his room from the field and it opens up space for us, and then we've got players to exploit that. And I hope we don't set them a hope and for a couple of goals as well, for the good and some faithful. For Moise Keyne. I think the woby, really, I think that's... Whenever you think Moise Keyne's ready or not, I don't think anyone's up for the start of the season thought he was going to score 20 goals this year. And I think in these games, these are the type of games where it's not going to be an overly physical side. It's a young side as well. I think he can come on with the woby behind him and I think the woby will put him in. All it takes is one goal to change him. Of course, the goal changes everything. And just finally, do you expect Anthony Gordon to be on the bench, or do you think he'll have... I don't know, because there'll be too many. Because then you'll have to fit Carvel Llew. It depends on who starts up front. I haven't got quite a lot of options. I know people probably think we need more options. I hope that does set me up front. But that's the problem. It's not great for Anthony Gordon, because you get that carrot and then it's taken away from you. But he's close. He's really close. I think over the Christmas period, you'll get at least a cut at the summer period. I'd like to see him go on loan in January, really, if we're not going to use him. I'll say it. There you go. Let us know what you think in the comments section below. Are you confident, if you're a never-thowning, that we can get back-to-back wins for the first time this season? If you're a Norwich fan, are you confident that you can come to Gouldersen and beat us? Let us know. Big thanks to Andy. Subscribe if you haven't. Get over to Peyton if you want more videos. Give the video a thumbs up. Thanks for watching. See you later.