Galilean equations for massless fields

TL;DR

This paper derives Galilei-invariant equations for massless fields by contracting relativistic wave equations, revealing a rich variety of physically relevant models including electromagnetic and Chern-Simons systems.

Contribution

It systematically classifies all linear and many non-linear Galilei-invariant equations for massless fields, expanding the understanding of non-relativistic field theories.

Findings

Multiple non-equivalent Galilei-invariant wave equations for spin 0 and 1

Connections between Lorentz and Galilei group representations

Classification of linear and non-linear Galilei-invariant equations

Abstract

Galilei-invariant equations for massless fields are obtained via contractions of relativistic wave equations. It is shown that the collection of non-equivalent Galilei-invariant wave equations for massless fields with spin equal 1 and 0 is very reach and corresponds to various contractions of the representations of the Lorentz group to those of the Galilei one. It describes many physically consistent systems, e.g., those of electromagnetic fields in various media or Galilean Chern-Simon models. Finally, classification of all linear and a big group of non-linear Galilei-invariant equations for massless fields is presented.