General algorithm for non-relativistic diffeomorphism invariance

TL;DR

This paper presents an algorithmic method for formulating non-relativistic diffeomorphism invariance involving matter and gauge fields, applicable to various abelian gauge interactions and demonstrated on 2D electron systems with external and Chern-Simons fields.

Contribution

It introduces a comprehensive step-by-step algorithm for non-relativistic diffeomorphism invariance applicable to matter and gauge fields, including abelian interactions.

Findings

Algorithm successfully applied to 2D electron systems

Handles external fields and Chern-Simons dynamics

Provides a unified framework for non-relativistic invariance

Abstract

An algorithmic approach towards the formulation of non-relativistic diffeomorphism invariance has been developed which involves both matter and gauge fields. A step by step procedure has been provided which can accommodate all types of (abelian) gauge interaction. The algorithm is applied to the problem of a two dimensional electron moving under an external field and also under the Chern-Simons dynamics.