Is there a standard way to define Canonical Transformations in the case of field theory or spacetime?
I saw that under ADM formalism it is possible to define a generating function: $$ G(t)= \sum_i p_i \delta q_i - H\delta t $$
But it's not clear what is the meaning of this generating function and why the transformations raise from it are canonical.
What's the definition of the scholarpedia article of the Poisson brackets $[A,B]$, how do they incorporate the time dimension into it?
