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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)].

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53D50 Geometric quantization
81S10 Geometry and quantization, symplectic methods
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References:

[1] Batalin, I., Vilkovisky, G.: Gauge algebra and quantization. Phys. Lett.102B, 27 (1981)
[2] Batalin, I., Vilkovisky, G.: Quantization of gauge theories with linearly dependent generators. Phys. Rev.D29, 2567 (1983)
[3] Witten, E.: A note on the antibracket formalism. Mod. Phys. Lett.A5, 487 (1990) · Zbl 1020.81931
[4] Schwarz, A.: The partition function of a degenerate functional. Commun. Math. Phys.67, 1 (1979) · Zbl 0429.58015
[5] Berezin, F.: Introduction to algebra and analysis with anticommuting variables. Moscow Univ., 1983 (English translation is published by Reidel) · Zbl 0527.15020
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