Schwarz, Albert Geometry of Batalin-Vilkovisky quantization. (English) Zbl 0786.58017 Commun. Math. Phys. 155, No. 2, 249-260 (1993). 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)]. Reviewer: C.S.Sharma (London) Cited in 2 ReviewsCited in 155 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 53D50 Geometric quantization 81S10 Geometry and quantization, symplectic methods Keywords:Batalin-Vilkovisky quantization; gauge; symplectic manifold × Cite Format Result Cite Review PDF Full Text: DOI arXiv 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) · doi:10.1103/PhysRevD.28.2567 [3] Witten, E.: A note on the antibracket formalism. Mod. Phys. Lett.A5, 487 (1990) · Zbl 1020.81931 · doi:10.1142/S0217732390000561 [4] Schwarz, A.: The partition function of a degenerate functional. Commun. Math. Phys.67, 1 (1979) · Zbl 0429.58015 · doi:10.1007/BF01223197 [5] Berezin, F.: Introduction to algebra and analysis with anticommuting variables. Moscow Univ., 1983 (English translation is published by Reidel) · Zbl 0527.15020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.