Note About Relational Mechanics of General Forms of Particle Actions

TL;DR

This paper demonstrates that particle interaction actions can be made invariant under gauged Galilean transformations, resulting in a Hamiltonian with simple form and gauge-generating constraints.

Contribution

It introduces a method to make general particle actions invariant under gauged Galilean transformations, simplifying the Hamiltonian structure.

Findings

Hamiltonian has a simple form with first class constraints.

Gauged Galilean invariance can be achieved for any particle interaction action.

Resulting gauge transformations are generated by the constraints.

Abstract

In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class constraints which are generators of corresponding gauge transformations included.