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

Understand

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.