The Classical Particle Coupled to External Electromagnetic Field ? Symmetries and Conserved Quantities

摘要

We consider a classical particle minimally coupled to an external electromagneticfield, in both non-relativistic and relativistic regimes. The coupling is constructedvia the electromagnetic potential which is assumed to satisfy the classical Maxwellequations. We review Noether’s theorem at classical level associating infinitesimalsymmetries to conserved quantities. The fundamental space-time symmetries areinvestigated considering a non-relativistic and a relativistic action in a particularreference frame. Considering some symmetry hypothesis on the action variation wework out in detail the corresponding conserved quantities.