Galilean Conformal Electrodynamics

TL;DR

This paper demonstrates that Galilean limits of Maxwell's Electrodynamics exhibit infinite-dimensional Galilean Conformal Symmetry in four dimensions, establishing a novel non-relativistic conformal field theory framework.

Contribution

It reveals that both electric and magnetic Galilean limits of Maxwell's equations are invariant under an infinite-dimensional Galilean Conformal Algebra in four dimensions, a first in higher-dimensional non-relativistic theories.

Findings

Galilean limits of Maxwell's equations are conformally invariant.

The symmetries form an infinite-dimensional algebra.

This provides the first example of an infinite Galilean Conformal Field Theory in D>2.

Abstract

Maxwell's Electrodynamics admits two distinct Galilean limits called the Electric and Magnetic limits. We show that the equations of motion in both these limits are invariant under the Galilean Conformal Algebra in D=4, thereby exhibiting non-relativistic conformal symmetries. Remarkably, the symmetries are infinite dimensional and thus Galilean Electrodynamics give us the first example of an infinitely extended Galilean Conformal Field Theory in D>2. We examine details of the theory by looking at purely non-relativistic conformal methods and also use input from the limit of the relativistic theory.