Hamiltonian Noether theorem for gauge systems and two time physics

TL;DR

This paper revisits the Hamiltonian Noether theorem for gauge systems, introducing a new method to link gauge transformations with conserved quantities from first class constraints, with applications to various physical models.

Contribution

It presents a novel approach to derive gauge transformations from conserved quantities in Hamiltonian constrained systems, enhancing understanding of gauge symmetries.

Findings

Gauge transformations generated by conserved quantities

Application to relativistic point particle and Friedberg model

Extension to two time physics

Abstract

The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al. model and, with special emphasis, to two time physics.