Galilei-invariant equations for massive fields

TL;DR

This paper derives and classifies Galilei-invariant equations for massive fields of various spins, showing their broad applicability and connection to relativistic equations through contraction methods.

Contribution

It provides a comprehensive list of Galilei-invariant wave equations for scalar and vector fields, highlighting their physical relevance and derivation methods.

Findings

The collection of Galilei-invariant equations is extensive and describes many physically consistent systems.

Galilei-invariant equations can be obtained via contraction from relativistic equations.

The approach allows modeling phenomena like spin-orbit and Darwin couplings in a Galilei-invariant framework.

Abstract

Galilei-invariant equations for massive fields with various spins have been found and classified. They have been derived directly, i.e., by using requirement of the Galilei invariance and various facts on representations of the Galilei group deduced in the paper written by de Montigny M, Niederle J and Nikitin A G, J. Phys. A \textbf{39}, 1-21, 2006. A completed list of non-equivalent Galilei-invariant wave equations for vector and scalar fields is presented. It shows two things. First that the collection of such equations is very broad and describes many physically consistent systems. In particular it is possible to describe spin-orbit and Darwin couplings in frames of Galilei-invariant approach. Second, these Galilei-invariant equations can be obtained either via contraction of known relativistic equations or via contractions of quite new relativistic wave equations.