ar X iv : h ep - t h / 92 10 13 5 v 2 2 8 O ct 1 99 2 Anticommuting Variables , Fermionic Path Integrals and Supersymmetry Lectures given at the XXVIII Karpacz Winter
نویسنده
چکیده
Fermionic Brownian paths are defined as paths in a space para-metrised by anticommuting variables. Stochastic calculus for these paths, in conjunction with classical Brownian paths, is described; Brownian paths on supermanifolds are developed and applied to establish a Feynman-Kac formula for the twisted Laplace-Beltrami operator on differential forms taking values in a vector bundle. This formula is used to give a proof of the Atiyah-Singer index theorem which is rigorous while being closely modelled on the supersymmetric proofs in the physics literature.
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تاریخ انتشار 1992