Galilean Geometry in Condensed Matter Systems

TL;DR

This paper develops a systematic approach to incorporate Galilean invariance into field theories, exploring its implications in effective field theory, fluid dynamics, and quantum Hall systems.

Contribution

It introduces a general framework for defining background geometries compatible with Galilean invariance in various physical contexts.

Findings

Established a method for implementing Galilean invariance in field theories.

Applied the framework to fluid dynamics and quantum Hall effect.

Provided new insights into the geometric structure underlying non-relativistic systems.

Abstract

We present a systematic means to impose Galilean invariance within field theory. We begin by defining the most general background geometries consistent with Galilean invariance and then turn to applications within effective field theory, fluid dynamics, and the quantum Hall effect.