Anticommuting Variables, Fermionic Path Integrals and Supersymmetry
摘要
(Replacement because mailer changed `hat' for supercript into something weird. The macro `\sp' has been used in place of the `hat' character in this revised version.) Fermionic Brownian paths are defined as paths in a space para\-metr\-ised 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.
关键词
引用
@article{arxiv.hep-th/9210135,
title = {Anticommuting Variables, Fermionic Path Integrals and Supersymmetry},
author = {Alice Rogers},
journal= {arXiv preprint arXiv:hep-th/9210135},
year = {2009}
}
备注
18 pages, KCL-TH-92-5