ar X iv : h ep - t h / 92 05 08 8 v 1 2 6 M ay 1 99 2 Geometry of Batalin - Vilkovisky quantization
نویسنده
چکیده
A very general and powerful approach to quantization of gauge theories was proposed by Batalin and Vilkovisky [1],[2]. The present paper is devoted to the study of geometry of this quantization procedure. The main mathematical objects under consideration are P -manifolds and SP -manifolds (supermanifolds provided with an odd symplectic structure and, in the case of SP -manifolds, with a volume element). The Batalin-Vilkovisky procedure leads to consideration of integrals of the form ∫ L Hdλ where L is a Lagrangian submanifold of an SP -manifold M and H satisfies the equation ∆H = 0 where ∆ is an odd analog of Laplacian. The choice of L can be interpreted as a choice of gauge condition; Batalin and Vilkovisky proved that in some sense their procedure is gauge independent. Namely they proved that ∫
منابع مشابه
ar X iv : h ep - t h / 97 03 05 4 v 1 6 M ar 1 99 7 Symmetries and the Antibracket : The Batalin - Vilkovisky Method
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The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q} = 0), a P -structure (odd symplectic structure ) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclass...
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تاریخ انتشار 2008