General algorithm for non-relativistic diffeomorphism invariance
Rabin Banerjee, Arpita Mitra, Pradip Mukherjee
TL;DR
The paper presents a systematic algorithm to achieve non-relativistic diffeomorphism invariance by locally gauging Galilean symmetry for theories with scalar and gauge fields. It introduces covariant derivatives and geometry-related fields, then reinterprets the localized theory as a curved-space, spatially diffeomorphic NRQFT grounded in Newton–Cartan geometry, with a preserved flat limit. The method is applied to a Schrödinger field in an external gauge field and to a CS gauge dynamics, demonstrating[curvature-induced modifications and] invariant formulations in curved space and addressing gauge symmetry issues. This framework provides a principled route to NRQFT in curved space, with potential implications for fractional quantum Hall physics and mesoscopic systems where diffeomorphism invariance is relevant.
Abstract
An algorithmic approach towards the formulation of non-relativistic diffeomorphism invariance has been developed which involves both matter and gauge fields. A step by step procedure has been provided which can accommodate all types of (abelian) gauge interaction. The algorithm is applied to the problem of a two dimensional electron moving under an external field and also under the Chern-Simons dynamics.