BFV quantization on hermitian symmetric spaces

E. S. Fradkin*, V. Ya Linetsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.

Original languageEnglish (US)
Pages (from-to)577-601
Number of pages25
JournalNuclear Physics, Section B
Volume444
Issue number3
DOIs
StatePublished - Jun 26 1995

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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