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

Oleg Yu. Shvedov

doi:10.1006/aphy.2002.6305

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

Oleg Yu. Shvedov

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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.

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Oleg Yu. Shvedov. 2001-11-29. On Correspondence of BRST-BFV, Dirac and Refined Algebraic Quantizations of Constrained Systems. https://doi.org/10.1006/aphy.2002.6305

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