Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry

TL;DR

This paper develops a dynamical field-theoretic realization of Newton-Cartan geometry by localizing Galilean symmetry, bridging the gap between algebraic structures and physical theories of nonrelativistic gravity.

Contribution

It introduces a novel dynamical realization of Newton-Cartan geometry through the localization of Galilean symmetry, which was previously only understood algebraically.

Findings

Provides a field-theoretic framework for Newton-Cartan geometry.

Shows how Galilean symmetry localization leads to Newton-Cartan structures.

Bridges algebraic and dynamical approaches to nonrelativistic gravity.

Abstract

Newtonian gravity was formulated as a geometrodynamic theory as far back in 1930s by Elie Cartan in what is named aptly as Newton Cartan space time. Though there are several approaches of realizing the algebraic structure of the Newton Cartan geometry from a contraction of the relativistic results, a dynamical (field theoretic) realization of it is lacking. In this paper we present such a realization from the localisation of the Galilean Symmetry of nonrelativistic matter field theories.