 029 Alice Rogers
 Supersymmetry and Brownian motion on supermanifolds
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Jan 4, 02

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Abstract. An anticommuting analogue of Brownian motion, corresponding to
fermionic quantum mechanics, is developed, and combined with
classical Brownian motion to give a generalised FeynmanKacIt\^o
formula for paths in geometric supermanifolds. This formula is
applied to give a rigorous version of the proofs of the
AtiyahSinger index theorem based on supersymmetric quantum
mechanics. It is also shown how superpaths, parametrised by a
commuting and an anticommuting time variable, lead to a manifestly
supersymmetric approach to the index of the Dirac operator. After
a discussion of the BFV approach to the quantization of theories
with symmetry, it is shown how the quantization of the topological
particle leads to the supersymmetric model introduced by Witten in
his study of Morse theory.
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