TY - JOUR

T1 - BFV quantization on hermitian symmetric spaces

AU - Fradkin, E. S.

AU - Linetsky, V. Ya

N1 - Funding Information:
One of the authors (E.S.E) would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste. This work was supported in part by the NATO Linkage Grant No. 931717.

PY - 1995/6/26

Y1 - 1995/6/26

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(95)00187-W

DO - 10.1016/0550-3213(95)00187-W

M3 - Article

AN - SCOPUS:0007286841

SN - 0550-3213

VL - 444

SP - 577

EP - 601

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -