Quantization of Galilean Electrodynamics: a non-trivially trivial theory

Abstract

We consider the quantization of the non-relativistic limit of electrodynamics called Galilean electrodynamics. To that end, we apply the Dirac bracket formalism to understand the constraints and dynamics of the theory and analyze its gauge structure. We show that the theory is fully constrained, which eliminates all the degrees of freedom from the path integral.