Discrete path integral for spin-1/2 in the Grassmannian representation

Details Discrete path integral for spin-1/2 in the Grassmannian representation Discrete path integral for spin-1/2 in the Grassmannian representation

2001-04-23

arxiv.org/abs/quant-ph/0104113v1

Physics

Quantum Physics

Latex; 12 pages, no figures

Scientific paper

A variation to the usual formulation of Grassmann representation path integrals is presented. Time-indexed anticommuting partners are introduced for each Grassmann coherent state variable and a general method for handling the effect of these introduced Grassmann partners is also developed. These Grassmann partners carry the nilpotency and anticommutivity of the Grassmann coherent state variables into the propagator and allow the propagator to be written as a path integral. Two examples are introduced in which this variation is shown to yield exact results. In particular, exact results are demonstratated for a spin-1/2 in a time-dependent magnetic field, and for a spin-boson system. The stationary path approximation is then shown to be exact for each example.

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