Journal
PHYSICAL REVIEW D
Volume 92, Issue 12, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.92.125036
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Funding
- U.S. Department of Energy [DE-SC0011637]
- Deutsche Forschungsgemeinschaft
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We give a covariant construction of Lagrangians for spinor fields in generic Newton-Cartan backgrounds. A nonrelativistic Dirac or Levy-Leblond operator and the associated fields are obtained from relativistic analogues by a limiting procedure. The relativistic symmetries induce the complete set of nonrelativistic symmetries, including Milne boosts and local Galilean transformations. The resulting Levy-Leblond operator includes nonminimal 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.
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