Is Canonical Momentum conserved?

[referframe]

Main Question or Discussion Point

Given a system of charged particles interacting with an EM field. Is the canonical momentum always conserved? If so, what is the associated symmetry?

Thanks in advance.

 

[vanhees71]

The canonical momentum is conserved, if the Hamiltonian is independent of the corresponding configuration variable. Then the system is symmetric under translations of this configuration variable.