A Feynman-Kac Formula for Anticommuting Brownian Motion

Details A Feynman-Kac Formula for Anticommuting Brownian Motion A Feynman-Kac Formula for Anticommuting Brownian Motion

2000-08-17

arxiv.org/abs/quant-ph/0008081v1

Physics

Quantum Physics

21 pages

Scientific paper

10.1088/0305-4470/34/3/315

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.

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