Refined Algebraic Quantization of Constrained Systems with Structure Functions

TL;DR

This paper generalizes the refined algebraic quantization method to systems with structure functions and open gauge algebras, proposing a new inner product prescription and exploring its relation to BRST-BFV quantization.

Contribution

It introduces a novel inner product approach for open-algebra systems and analyzes the connection with BRST-BFV quantization.

Findings

New inner product prescription for open-algebra systems

Illustration of the method on a simple example

Analysis of correspondence with BRST-BFV quantization

Abstract

The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained systems with structure functions and open gauge algebras. A new prescription for inner product for the open-algebra systems is suggested. It is illustrated on a simple example. The correspondence between refined algebraic and BRST-BFV quantizations is investigated for the case of nontrivial structure functions.