BFV approach to geometric quantization

E. S. Fradkin*, V. Ya Linetsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Original languageEnglish (US)
Pages (from-to)569-621
Number of pages53
JournalNuclear Physics, Section B
Volume431
Issue number3
DOIs
StatePublished - Dec 12 1994

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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