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.


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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[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 · doi:10.1007/BF02097392
[3] Witten, E.: A note on the antibracket formalism. Mod. Phys. LettA5, 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] 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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