BFV quantization on hermitian symmetric spaces |
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| Institution: | 1. International Center for Advanced Science and Technology (ICAST), P.O. Box 4239, Ann Arbor, MI 48106, USA;2. P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky Prospect 53, Moscow 117924, Russian Federation;1. Service de chirurgie maxillo-faciale et stomatologie, chirurgie plastique et réparatrice, chirurgie de la main, CHU, hôpital Bocage-Central, rue Gaffarel, 21000, Dijon, France;2. Laboratoire EA 4268 4IS, université de Franche-Comté, place Saint-Jacques, 35000, Besançon, France;3. Service de chirurgie maxillo-faciale et stomatologie, centre François-Xavier Michelet, CHU de Bordeaux, 33076, Bordeaux cedex, France;1. College of Materials Science and Engineering, Xi’an University of Architecture and Technology, Xi’an, China;2. College of urban construction, Wuchang University of Technology, Wuhan, China;3. National Dam Safety Research Center (Yangtze River Scientific Research Institute), Wuhan, China;4. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China;1. Structural Biology Brussels, Vrije Universiteit Brussel (VUB), Brussels, Belgium;2. VIB-VUB Center for Structural Biology, VIB, Brussels, Belgium |
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| 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. |
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