On nonrelativistic 3D Spin-1 theories
Eric A. Bergshoeff, Jan Rosseel, Paul K. Townsend
TL;DR
This paper explores nonrelativistic limits of 3D spin-1 theories, deriving Schrödinger equations from Proca models and connecting them to 4D Maxwell equations, with brief considerations of spin-2 extensions.
Contribution
It introduces a novel nonrelativistic limit procedure for 3D spin-1 theories and relates them to null reductions of 4D Maxwell equations.
Findings
Nonrelativistic 3D Proca theories lead to spin-1 Schrödinger equations.
Null reduction of 4D Maxwell equations yields similar nonrelativistic spin-1 theories.
Brief discussion on extending the approach to spin-2 theories.
Abstract
We describe non-relativistic limits of the 3D Proca and square-root Proca theories that yield spin-1 Schroedinger equations. Analogous results are found by generalized null reduction of the 4D Maxwell or complex self-dual Maxwell equations. We briefly discuss the extension to spin-2.
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