Gauge Functions and Galilean Invariance of Lagrangians

TL;DR

This paper introduces a new method using null Lagrangians and gauge functions to ensure Galilean invariance of Lagrangians, with potential implications for gauge theories in physics.

Contribution

The paper develops a novel approach to achieve Galilean invariance in Lagrangians using null Lagrangians and gauge functions, addressing an old physics problem.

Findings

Demonstrates Galilean invariance of Newton's inertia Lagrangian

Proposes a general method applicable to gauge-based theories

Suggests broader implications for physics theories

Abstract

A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is suggested that this new solution of an old physics problem may have implications and potential applications to all gauge-based theories of physics.