Reparametrization Invariance as Gauge Symmetry

TL;DR

This paper explores reparametrization invariance as a gauge symmetry, analyzing its peculiarities, gauge fixing, and the relation to zero-Hamiltonian systems, providing insights into the structure of such invariances.

Contribution

It offers a detailed analysis of reparametrization invariance as gauge symmetry, including gauge fixing procedures and the connection to zero-Hamiltonian phenomena.

Findings

Reparametrization invariance can be treated as a gauge symmetry with specific peculiarities.

Different gauge choices correspond to different reference frames in classical systems.

A general structure of reparametrizations and their relation to zero-Hamiltonian systems is established.

Abstract

Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of reparametrization invariant systems in which one fixes the gauge on the classical level by means of time-dependent gauge conditions. In such an approach one can interpret different gauges as different reference frames. We discuss the relations between different gauges and the problem of gauge invariance in this case. Finally, we establish a general structure of reparametrizations and its connection with the zero-Hamiltonian phenomenon.