Take the tour ×  Where does the factor $\frac{1}{T}$ ($T$ is the
string tension) in this Poisson bracket come from?  $$
\{X^{\mu}(\tau,\sigma),\dot{X}^{\nu}(\tau,\sigma')\} ~=~
\frac{1}{T}\delta(\sigma-\sigma')\eta_{\mu\nu}. $$  I think I
can see from remembering the definition of a Poisson bracket
(for example in canonical coordinates) why in terms of momentum
we have  $$ \{P^{\mu}(\tau,\sigma),X^{\nu}(\tau,\sigma')\} ~=~
\delta(\sigma-\sigma')\eta_{\mu\nu} $$  but I don't see why this
factor in the first equation has to be there.  In addition to
deriving it by calculation, is there an intuitive physical way
how one can see why the factor of inverse tension has to be
there, similar to explaining the appearance of the tension in
front of the integral in the action by the fact that it costs
energy to stretch the world-sheet?  share|improve this question
I somehow feel very stupid that I dont see this :-/ –  Dilaton
Mar 15 at 12:06 Dimensional analysis? –  Michael Brown Mar 15 at
12:17 @MichaelBrown Maybe ... b