On the gauge symmetries of the spinning particle

TL;DR

This paper analyzes the gauge symmetries of the spinning particle using Noether identities, revealing a simple Lie algebra structure for both massless and massive cases, and introduces a decoupled Fermionic gauge transformation.

Contribution

It provides a systematic Lagrangian-based method to identify gauge symmetries of the spinning particle, including a new Fermionic transformation with a simple algebraic structure.

Findings

Identified a simple Lie algebra structure for gauge transformations

Discovered a decoupled Fermionic gauge transformation

Field redefinitions allow direct derivation of gauge algebra

Abstract

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local Bosonic and Fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new Fermionic gauge transformation of the "position" and "spin" variables in the action decouples from that of the "einbein" and "gravitino". It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases.