Constrained Hamiltonian analysis of a non relativistic Schrodinger field coupled with C-S gravity

TL;DR

This paper performs a constrained Hamiltonian analysis of a non-relativistic Schrödinger field coupled with Chern-Simons gravity in 2+1 dimensions, emphasizing the importance of Galilean gauge theory for consistent coupling.

Contribution

It introduces a Hamiltonian framework for non-relativistic Schrödinger fields coupled with Chern-Simons gravity using Galilean gauge theory, highlighting the necessity of this approach.

Findings

Deviations from Galilean gauge theory lead to inconsistent models.

The analysis confirms the role of Galilean gauge theory in non-relativistic gravity coupling.

Discussion on nonrelativistic spatial diffeomorphism issues.

Abstract

We provide a constrained Hamiltonian analysis of a non relativistic Schrodinger field in 2+1 dimensions , coupled with Chern - Simons gravity. The coupling is achieved by the recently advanced Galilean gauge theory \cite{BMM1},\cite{ BMM2}, \cite{BM4}. The calculations are repeated with a truncated model to show that deviation from Galilean gauge theory makes the theory untenable. The issue of nonrelativistic spatial diffeomorphism is discussed in this context.