Wednesday, 6 April 2016

lagrangian formalism - Is there a general formula to translate from *canonical* to *physical* momentum?


In Peskin and Schroeder, after having derived a conserved tensor Tμν associated with translations in space-time (the stress-energy tensor), it is said that the charges d3xT0i: Pi=d3xiiπ(x)iϕ(x)

are to be "interpreted" as the physical momentum, as opposed to the canonical momentum, whose density is


π(x) = L˙ϕ(x).


Is there a way of showing that the above equation does indeed correspond to the physical momentum?





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