Galilei invariant theories. III. Wave equations for massless fields

TL;DR

This paper derives Galilei-invariant wave equations for massless fields by contracting relativistic equations, revealing a wide variety of physically consistent equations for spin 0 and 1 fields.

Contribution

It introduces a comprehensive set of Galilei-invariant wave equations for massless fields, expanding the understanding of non-relativistic limits of relativistic wave equations.

Findings

Many non-equivalent Galilei-invariant equations for massless fields with spin 0 and 1.

Existence of numerous equations corresponding to different contractions of Lorentz group representations.

Demonstration of physically consistent systems described by these 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 broad and describes many physically consistent systems. In particular, there exist a huge number of such equations for massless fields which correspond to various contractions of representations of the Lorentz group to those of the Galilei one.