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Journal of Physics A Mathematical and General

The path integral for arbitrary fermion sectors in supersymmetric quantum mechanics

M O'Connor

Published Feb 21, 1991• 1 citation
Publisher

Abstract

Shows how to obtain the kernel for arbitrary fermion sectors in supersymmetric quantum mechanics by applying standard coordinate space functional integral techniques to the coherent state fermionic path integral.
DOI
10.1088/0305-4470/24/4/021

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In the zero-fermion and n-fermion sectors of Euclidean supersymmetric quantum theories on an n-dimensional manifold a transformation is known which reduces the functional integrals to Gaussian functional integrals. The transformation, often called a Nicolai map, can be interpreted as a Markovian stochastic process. We investigate two different possibilities to generalize this result to an arbitrary p-fermion sector (0\ensuremath{\le}p\ensuremath{\le}n), and find that only one of them is viable, in general. We give a general representation of the solution of the Schr\"odinger equation in the p-fermion sector in terms of a Markovian stochastic process which extends the stochastic process of the zero- and n-fermion sectors.
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