Spinor fields in general Newton-Cartan backgrounds

TL;DR

This paper develops a covariant framework for spinor fields in Newton-Cartan backgrounds, deriving non-relativistic operators and symmetries from relativistic limits, with implications for gauge couplings and phenomenology.

Contribution

It introduces a covariant construction of spinor Lagrangians in Newton-Cartan geometries, including a non-relativistic Dirac operator with non-minimal couplings derived from relativistic theories.

Findings

Derivation of a non-relativistic Dirac/Levy-Leblond operator from relativistic analogues.

Identification of complete non-relativistic symmetry set, including Milne boosts.

Fixing the gyromagnetic ratio to g=1 in generic cases, with special considerations in three dimensions.

Abstract

We give a covariant construction of Lagrangians for spinor fields in generic Newton-Cartan backgrounds. A non-relativistic Dirac/Levy-Leblond operator and the associated fields are obtained from relativistic analogues by a limiting procedure. The relativistic symmetries induce the complete set of non-relativistic symmetries, including Milne boosts and local Galilean transformations. The resulting Levy-Leblond operator includes non-minimal couplings to the Newton-Cartan structure as well as to the gauge field, and with these couplings it transforms covariantly. Phenomenologically, this fixes the gyromagnetic ratio to g=1. Three-dimensional spacetimes are an exception: generic g is possible but results in modified Milne transformations, which - upon gauge fixing - reproduces the anomalous diffeomorphisms found in earlier approaches.