How to Choose a Gauge? The Case of Hamiltonian Electromagnetism

Abstract We develop some ideas about gauge symmetry in the context of Maxwell’s theory electromagnetism Hamiltonian formalism. One great benefit this formalism is that it pairs momentum and configurational degrees freedom, so a decomposition one side into subsets can be translated other. In case electromagnetism, enables us to pair freedom electric field with vector potential. Another algorithmically identifies equations motion represent time-dependent symmetries. For these two benefits allow define gauge-fixing parallel special decompositions field. More specifically, we apply Helmholtz theorem split its Coulombic radiative parts, show how gives role Coulomb (i.e. div $$(\mathbf{A}) = 0$$ ( A ) = 0 ). relate argument Maudlin’s (Entropy, 2018. https://doi.org/10.3390/e20060465 ) discussion, which advocated gauge.