Geometry of Batalin-Vilkovisky quantization. (English) Zbl 0786.58017

An odd symplectic manifold is called a \(P\)-manifold and a \(P\)-manifold equipped with a volume element is called an \(SP\)-manifold. The author provides a complete classification of these manifolds and uses the classification to prove some results concerning the procedure of quantization introduced by I. Batalin and G. Vilkovisky [Phys. Lett., B 102, 27-31 (1981)].


37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53D50 Geometric quantization
81S10 Geometry and quantization, symplectic methods
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[1] Batalin, I., Vilkovisky, G.: Gauge algebra and quantization. Phys. Lett.102B, 27 (1981)
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