On Admissible Gauges for Constrained Systems

TL;DR

This paper compares gauge-fixing and gaugeless methods for reducing phase space in Hamiltonian systems, proposing a new class of admissible gauges called canonical gauges that depend only on ignorable coordinates.

Contribution

It introduces the concept of canonical gauges as a subclass of admissible gauges, based on a gaugeless reduction approach that constructs the reduced phase space without fixing gauges.

Findings

Gaugeless approach constructs reduced phase space locally without gauge fixing.

Canonical gauges depend only on ignorable coordinates.

A practical method to identify canonical gauges is proposed.

Abstract

The {\it {gauge - fixing} } and {\it gaugeless } methods for reducing the phase space in the generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges . In the gaugeless approach, the reduced phase space of a Hamiltonian system with the first class constraints is constructed locally, without any gauge fixing, using the following procedure: abelianization of constraints with the subsequent canonical transformation so that some of the new momenta are equal to the new abelian constraints. As a result the corresponding conjugate coordinates are ignorable ( nonphysical ) one while the remaining canonical pairs corresponds to the true dynamical variables. This representation for the phase space prompts us the definition of subclass of admissible gauges -- canonical gauges as functions depending only on the ignorable coordinates. A practical method to recognize the canonical gauge is proposed .