Solving Gauge Invariant Systems without Gauge Fixing: the Physical Projector in 0+1 Dimensional Theories

TL;DR

This paper introduces a gauge-invariant quantization method using the physical projector, avoiding gauge fixing, and demonstrates its effectiveness on SO(2) and SO(3) gauge systems, simplifying spectral analysis.

Contribution

It applies the physical projector approach to quantum mechanical gauge systems, providing a straightforward analysis without gauge fixing, and extends understanding of spectra for SO(2) and SO(3).

Findings

Successfully characterized physical spectra for SO(2) and SO(3) gauge groups.

Avoided gauge fixing and additional degrees of freedom in quantization.

Method is based on standard coherent states and group theory, generalizable to other Lie algebras.

Abstract

The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones---two characteristic features of all other available methods for quantising constrained dynamics---is put to work in the context of a general class of quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge groups are considered specifically, and a comprehensive understanding of the corresponding physical spectra is achieved in a straightforward manner, using only standard methods of coherent states and group theory which are directly amenable to generalisation to other Lie algebras. Results extend by far the few examples available in the literature from much more subtle and delicate analyses implying gauge fixing and the characterization of modular space.