Galilean Electrodynamics: Covariant formulation and Lagrangian

TL;DR

This paper develops a covariant Lagrangian framework for Galilean electrodynamics, unifying its limits and exploring symmetries within Newton-Cartan geometry, including invariance under Galilean conformal algebra.

Contribution

It introduces a covariant Lagrangian formalism for Galilean electrodynamics and analyzes its symmetry properties, which is a novel approach in this area.

Findings

Constructed a unified Lagrangian for Galilean electrodynamics.

Demonstrated invariance under Galilean conformal algebra in four dimensions.

Calculated the energy-momentum tensor within the formalism.

Abstract

In this paper, we construct a single Lagrangian for both limits of Galilean electrodynamics. The framework relies on a covariant formalism used in describing Newton-Cartan geometry. We write down the Galilean conformal algebra and its representation in this formalism. We also show that the Lagrangian is invariant under the Galilean conformal algebra in d = 4 and calculate the energy-momentum tensor.