BFV quantization on Hermitian symmetric spaces. (English) Zbl 0990.81532
Summary: 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.
MSC:
| 81S10 | Geometry and quantization, symplectic methods |
| 37J05 | Relations of dynamical systems with symplectic geometry and topology (MSC2010) |
| 58Z05 | Applications of global analysis to the sciences |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T70 | Quantization in field theory; cohomological methods |
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