Hamiltonian analysis of the Schroedinger field coupled with dynamic non-relativistic gravity

TL;DR

This paper develops a Hamiltonian framework for a Schrödinger field coupled with a dynamical Newtonian gravity in Newton-Cartan spacetime, analyzing its constraints, symmetries, and establishing its uniqueness.

Contribution

It introduces a novel Hamiltonian analysis of Schrödinger field interacting with dynamical non-relativistic gravity using Galilean gauge theory, demonstrating the model's uniqueness.

Findings

The model's constraints are fully characterized.

Symmetries of the coupled system are explicitly verified.

The model and its constraints are shown to be unique in the literature.

Abstract

Using the recently mooted Galilean gauge theory we have constructed the model for the Schroedinger field interacting wuth gravity which is also dynamical. The dynamics of gravity is dictated by the Newtonian action in the Newton-Cartan spacetime. The theory is highly constrained . An elaborate analysis of the constraints of the theory have been performed. The symmetries are explicitly verified and the uniqueness of the model has been established. To the best of our knowledge both the model and its constraints structure are unique in the literature