Spinor fields in general Newton-Cartan backgrounds
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.
Cite
@article{arxiv.1510.03852,
title = {Spinor fields in general Newton-Cartan backgrounds},
author = {John F. Fuini and Andreas Karch and Christoph F. Uhlemann},
journal= {arXiv preprint arXiv:1510.03852},
year = {2016}
}
Comments
22 pages