Demystification of Non-relativistic Theories in Curved Background

TL;DR

This paper introduces galilean gauge theory, a new formalism for systematically constructing non-relativistic theories in curved backgrounds, specifically on Newton-Cartan manifolds, demonstrated through the example of a free particle.

Contribution

It presents a systematic algorithm for deriving covariant non-relativistic theories in curved space, based on gauging galilean symmetry, which was not previously established.

Findings

Provides a formalism for non-relativistic theories in curved backgrounds.

Demonstrates the method with a free particle example.

Establishes a connection to Newton-Cartan geometry.

Abstract

We discuss a new formalism for constructing a non-relativistic (NR) theory in curved background. Named as galilean gauge theory, it is based on gauging the global galilean symmetry. It provides a systematic algorithm for obtaining the covariant curved space time generalisation of any NR theory defined in flat space time. The resulting background is just the Newton- Cartan manifold. The example of NR free particle is explicitly demonstrated.