Thursday, 14 June 2018

classical electrodynamics - What is the conserved canonical momentum for a relativistically moving charge in a static Coulomb electric field?



The canonical momentum is a fundamental conserved quantity from Noether's theorem for translational invariance of the Lagrangian. Yet I'm finding it very difficult to see its derivation, or even a statement of what it is for something as fundamental as a relativistically moving charge in a static Coulomb electric field.


Can anyone state what it is, or even give a derivation if it's not too much trouble?




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