quantum particle physics quantum quantum field theory essence describes light matter interact theory agreement quantum mechanics special achieved describes phenomena involving electrically charged particles interacting means exchange represents quantum counterpart classical giving complete account matter light interaction technical terms described theory electromagnetic quantum vacuum called jewel physics extremely accurate predictions quantities like magnetic moment electron lamb shift energy levels hydrogen history quantum theory describing radiation matter interaction attributed british scientist 1920s able spontaneous described electromagnetic field ensemble introduction concept creation operators particles following years contributions elegant quantum came believe principle possible perform physical process involving charged particles studies revealed reliable order theory problem pointed higher orders series emerged making meaningless casting doubts internal consistency theory solution problem known time appeared fundamental existed special quantum mechanics difficulties theory increased end improvements microwave technology possible precise measurements shift levels hydrogen known lamb shift magnetic moment electron experiments exposed theory unable explain indication possible way given traveling train reach new_york giving talk conference subject completed non shift lines hydrogen measured lamb despite limitations agreement excellent idea simply attach mass charge actually fixed finite value experiments way absorbed yield finite result good agreement experiments procedure named based fundamental papers subject finally possible fully finite order series quantum jointly awarded nobel prize physics work area contributions gauge quantum allow order theory mathematical technique based initially different field operator based approach later showed approaches equivalent need attach physical meaning certain appearing theory subsequently fundamental aspects quantum field theory come seen criterion theory general works practice entirely comfortable mathematical validity referring shell game served model template subsequent quantum field theories subsequent theory quantum began early 1960s attained present form work building pioneering work independently showed weak nuclear force quantum merged single force view quantum introduction near end life gave series lectures intended lay public lectures published strange theory light matter classic non mathematical exposition point view articulated key components presentation basic actions goes place time place time electron goes place time place time electron certain place time actions represented form visual basic elements line straight line electron junction straight lines representing absorption electron seen adjacent important interpret implied particle gets point imply particles moving straight curved lines imply particles moving fixed speeds fact represented convention line straight imply thought electron images symbols represent actions point point absorb know things happen theory tells things happening visual actions introduces kind numerical quantities called probability probability square total probability moves place time place time associated quantity written similar quantity electron moving written quantity tells probability absorption calls related measured electron charge based assumption complex interactions represented fitting suitable collection building blocks probability probability complex interaction turns basic idea communicated making assumption square total probability mentioned acts like everyday probability book later corrected include specifically quantum style mathematics following basic rules probability event happen variety different ways probability sum probability possible ways process involves number independent sub processes probability product component probability basic constructions suppose start electron certain place time place time given arbitrary label place time given label typical question physical standpoint probability finding electron place later time place time simplest process achieve end electron elementary action elementary action knowledge probability sub processes expect probability happening rule gives simple estimated overall probability squared estimated probability ways end result come electron place time detected new moves probability complex process calculated knowing probability individual actions electron actions actions absorption expect find total probability probability actions chosen positions rule add probability alternatives elementary practice involves integration possibility electron moves goes electron moves moving probability possibilities points better total probability adding probability possibilities original simple estimate incidentally given process interacting electron way scattering infinite number intermediate processes absorbed emitted possibilities describing implies complex resulting probability provided case complicated contributes result matter time effort find accurate answer wants original question basic approach probability interactive process matter noting possible ways process constructed basic elements involves calculation involving definite rules find associated probability basic remains moves quantum description conceptual changes needed expect everyday life constraints points particle true quantum possibility electron moving basic action place time universe includes places reached speeds greater light earlier times electron moving backwards time viewed moving forward time probability quantum mechanics introduces important change way represented usual real numbers use everyday world square probability probability complex numbers avoids exposing reader mathematics complex numbers simple accurate representation arrows piece paper screen confused arrows actually simplified representations dimensions relationship points dimensions space time arrows fundamental description world given quantum theory satisfactory reason given needed accept essential description quantum phenomena related everyday ideas probability simple rule probability event square length corresponding arrow given process probability involved probability process given formula formula rules regards adding expect add instead add probability complex numbers addition familiar operations theory complex numbers given figures sum found follows let start second arrow end sum arrow goes directly start end second product arrows arrow length product lengths direction product found adding angles turned relative reference direction gives angle product turned relative reference direction change probability mathematics changing basic approach change fails account fact space time taken account actually consists complex numbers probability arrows minor changes quantity rotated multiple interest detailed associated fact electron small necessary detail connected fact electron statistics basic rule probability given complex process involving electron include exchange electron events resulting reverse negative simplest case starting ending calculated difference expect everyday idea sum finally corresponding probability electron respectively essentially solutions describes behavior electron probability gordon equation describes behavior probability called translation commonly standard literature follows formula symbol formula stands real numbers time position dimensions point labeled mass problem arose historically held progress years start assumption basic simple actions rules game want probability electron account possible ways possible end points way electron travels moving kind thing twice short like situation look closely line breaks collection simple lines looked closely turn composed simple lines difficult situation handle adding detail altered things slightly bad disaster struck found simple correction mentioned led infinite probability time problem fixed technique remained unhappy calling process conclusions framework able high degree accuracy properties magnetic moment points fails totally explain particles electron masses theory adequately explains numbers use numbers theories don understand come believe fundamental point view interesting problem mathematics gauge theory symmetry group gauge field interaction charged fields electromagnetic field field interacting electromagnetic field given real formula formula field particles electron field formula called psi bar referred formula gauge derivative constant equal electric charge field mass electron formula potential electromagnetic field generated electron formula external field imposed external source formula electromagnetic field motion begin definition gives formula substitute equation motion field find field terms formula formula equation results formula formula bringing middle term right hand transforms second equation left hand like original equation right hand interaction electromagnetic field important equation found equation time field formula terms time formula formula terms substituted impose gauge condition divergence potential formula formula wave equation potential version classical gauge equation square represents operator interaction picture theory treating sectors free permits build set states start probability different processes order evolution operator given initial state formula final state formula way formula technique known matrix evolution operator obtained interaction picture time evolution given interaction integral space second term density given formula formula time ordering operator evolution operator meaning series series fine structure constant development series called series despite conceptual clarity approach early textbooks follow presentation performing calculations easier work transforms experimental tests quantum typically scattering experiments scattering theory particles positions considered convenient think particles created annihilated interact look lines different interpretations electron line represents electron given energy momentum similar interpretation line represents electron creation absorption creation having specified energies terms series terms matrix quantum technique case rules drawing following rules add closed loops implies integration formula internal virtual particles constrained specific energy momentum usually required special article details probability given example scattering electron undergoing elastic scattering case able corresponding order series matrix formula able cross section scattering higher order terms evolution operator terms display containing following simpler ones closed loops imply presence having mathematical meaning overcome difficulty technique called devised producing finite results close agreement experiments important note criterion theory meaningful number finite case theory said reason needs finite number maintain value theory untouched exactly case quantum displaying procedure gives close agreement experiment seen electron ratio essential criterion quantum field theory considered viable theories describing fundamental interactions quantum counterpart presently active research theories series argument shows radius convergence series zero basic argument goes follows constant negative equivalent force constant negative reverse electromagnetic interaction like charges attract unlike charges repel render vacuum unstable decay cluster universe cluster universe theory sick negative value constant series converge series modern perspective defined quantum field theory high energy constant runs infinity finite energy signalling pole problem essentially appears suffer quantum issues motivations grand unified theory books louis sur des research quantum theory france new isbn isbn walter gauge theory weak interactions isbn kane gordon isbn miller isbn quantum vacuum introduction quantum isbn men isbn julian isbn gilbert introduction isbn journals popular lectures quantum lectures
Quantum electrodynamics