On Correspondence of BRST-BFV, Dirac and Refined Algebraic Quantizations of Constrained Systems

TL;DR

This paper explores the relationships between different quantization methods for constrained systems, establishing correspondences and generalizations, and addressing topological issues in the BRST-BFV, Dirac, and refined algebraic approaches.

Contribution

It demonstrates the correspondence between BRST-BFV, Dirac, and refined algebraic quantizations, including extensions to open algebras and nontrivial structure functions, with a new perspective on inner products.

Findings

Component of BFV wave function relates to refined algebraic quantization

Derived Giulini-Marolf group averaging formula from BRST-BFV prescription

Extended quantization correspondence to open algebras with structure functions

Abstract

Correspondence between BRST-BFV, Dirac and refined algebraic (group averaging, projection operator) approaches to quantize constrained systems is analyzed. For the closed-algebra case, it is shown that the component of the BFV wave function with maximal (minimal) number of ghosts and antighosts in the Schrodinger representation may be viewed as a wave function in the refined algebraic (Dirac) quantization approach. The Giulini-Marolf group averaging formula for the inner product in the refined algebraic quantization approach is obtained from the Batalin-Marnelius prescription for the BRST-BFV inner product which should be generally modified due to topological problems. The considered prescription for the correspondence of states is observed to be applicable to the open-algebra case. Refined algebraic quantization approach is generalized then to the case of nontrivial structure functions. A simple example is discussed. Correspondence of observables in different quantization methods is also investigated.