## Semiclassical approximation in Batalin-Vilkovisky formalism.(English)Zbl 0855.58005

Summary: 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 (1983) to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.

### MSC:

 58A50 Supermanifolds and graded manifolds 81T13 Yang-Mills and other gauge theories in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 53D50 Geometric quantization
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### References:

 [1] Batalin, I., Vilkovisky, G.: Gauge algebra and quantization. Phys. Lett.102B, 27 (1981); Quantization of gauge theories with linearly dependent generators. Phys. Rev.D29, 2567 (1983) [2] Schwarz, A.: Geometry of Batalin-Vilkovisky quantization. Commun. Math. Phys.155, 249 (1993) · Zbl 0786.58017 [3] Witten, E.: A note on the antibracket formalism. Mod. Phys. LettA5, 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] Witten, E.: TheN matrix model and gaugedWZW models. Preprint IASSNS-HEP-91126 [6] Dold, A.: Lectures on algebraic topology. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0234.55001
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