Hidden Symmetries in Second Class Constrained Systems - Are New Fields Necessary?

TL;DR

This paper demonstrates that for many second class constrained systems, gauge invariances can be uncovered within the original phase space without introducing additional fields, simplifying their analysis.

Contribution

It provides a general proof that extending phase space with new variables is unnecessary for revealing gauge invariances in second class constrained systems.

Findings

Gauge invariances can be identified in the original phase space.

Extension of phase space by new variables is not needed.

The proof applies to a broad class of systems with two second class constraints.

Abstract

For many systems with second class constraints, the question posed in the title is answered in the negative. We prove this for a range of systems with two second class constraints. After looking at two examples, we consider a fairly general proof. It is shown that, to unravel gauge invariances in second class constrained systems, it is sufficient to work in the original phase space itself. Extension of the phase space by introducing new variables or fields is not required.