Projection operator approach to general constrained systems

TL;DR

This paper introduces a novel BRST-like quantization method for constrained systems that does not require separating constraints into first and second class, potentially enabling covariant quantization of complex models.

Contribution

It presents a new quantization approach using an invariant projection operator, eliminating the need for constraint classification or conversion.

Findings

Method successfully applies to models without explicit first/second class separation.

Enables covariant quantization of complex constrained systems.

Provides an example demonstrating the approach's effectiveness.

Abstract

We propose a new BRST-like quantization procedure which is applicable to dynamical systems containing both first and second class constraints. It requires no explicit separation into first and second class constraints and therefore no conversion of second class constraints is needed. The basic ingredient is instead an invariant projection operator which projects out the maximal subset of constraints in involution. The hope is that the method will enable a covariant quantization of models for which there is no covariant separation into first and second class constraints. An example of this type is given.