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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:

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