Projection Operator Approach to Constrained Systems

TL;DR

This paper discusses Klauder's projection operator method for quantizing constrained systems, highlighting its advantages such as avoiding gauge fixing and Gribov problems, confirmed through simple examples.

Contribution

It clarifies that Klauder's approach effectively handles gauge invariance without gauge fixing or Gribov issues, supported by explicit examples.

Findings

Avoids gauge fixing conditions

Eliminates Gribov problems

Provides admissible integration over gauge orbits

Abstract

Recently, within the context of the phase space coherent state path integral quantisation of constrained systems, John Klauder introduced a reproducing kernel for gauge invariant physical states, which involves a projection operator onto the reduced Hilbert space of physical states, avoids any gauge fixing conditions, and leads to a specific measure for the integration over Lagrange multipliers. Here, it is pointed out that this approach is also devoid of any Gribov problems and always provides for an effectively admissible integration over all gauge orbits of gauge invariant systems. This important aspect of Klauder's proposal is explicitly confirmed by two simple examples.