Canonical Formalism of Non-Relativistic Theories Coupled to Newton-Cartan Gravity

TL;DR

This paper performs a canonical analysis of non-relativistic theories coupled to Newton-Cartan gravity, identifying degrees of freedom and analyzing their constraint structures to deepen understanding of their fundamental properties.

Contribution

It provides the first detailed canonical formulation of Schrödinger and non-relativistic electrodynamics within Newton-Cartan gravity, clarifying their physical degrees of freedom.

Findings

Identified the physical degrees of freedom in the theories.

Analyzed the constraint structure of coupled non-relativistic theories.

Clarified the canonical formulation of these theories.

Abstract

In this short note we perform canonical analysis of Schrodinger field and non-relativistic electrodynamics coupled to Newton-Cartan gravity. We identify physical degrees of freedom and analyze constraints structure of these theories.