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.

22 pages

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• Non-relativistic Reduction of Spinors, New Currents and their Algebra
• Symmetries and Couplings of Non-Relativistic Electrodynamics
• Galilean Geometry in Condensed Matter Systems
• Developments in non-relativistic field theory and complexity