On the question of symmetries in non-relativistic diffeomorphism invariant theories

TL;DR

This paper introduces a new algorithm to couple Galilean invariant models with curved spatial backgrounds by deriving them from relativistic theories, resolving previous ambiguities and ensuring symmetry in the flat limit.

Contribution

It presents a novel method to obtain Galilean invariant theories on curved backgrounds from relativistic models, addressing and resolving longstanding ambiguities.

Findings

Successfully couples Galilean models with curved backgrounds.

Ensures Galilean symmetry in the flat limit.

Resolves ambiguities and anomalies in nonrelativistic diffeomorphic theories.

Abstract

A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields. That the twin requirements are fulfilled is ensured by a new field, the existence of which was demonstrated recently from Galilean gauge theory. The ambiguities and anomalies concerning the recovery of Galilean symmetry in the flat limit of spatial non relativistic diffeomorphic theories, reported in the literature, are focused and resolved from a new angle.