Non-relativistic fields from arbitrary contracting backgrounds

TL;DR

This paper develops a systematic approach to derive non-relativistic field theories of various spins from relativistic theories on Newton-Cartan backgrounds, clarifying their geometric and gauge structures.

Contribution

It introduces a non-relativistic contraction method for fields of spins 0 to 3/2 coupled to gravity, extending previous work and clarifying the origin of Newton-Cartan gauge fields.

Findings

Derived non-relativistic field theories for spins 0 to 3/2

Clarified the origin of the Newton-Cartan central charge gauge field

Connected particle number conservation to the gauge structure

Abstract

We discuss a non-relativistic contraction of massive and massless field theories minimally coupled to gravity. Using the non-relativistic limiting procedure introduced in our previous work, we (re-)derive non-relativistic field theories of massive and massless spins 0 to 3/2 coupled to torsionless Newton-Cartan backgrounds. We elucidate the relativistic origin of the Newton-Cartan central charge gauge field $m_\mu$ and explain its relation to particle number conservation.