paper

Many-Body Diffusion and Path Integrals for Identical Particles

arXiv:cond-mat/9601079 · doi:10.1103/PhysRevE.53.4467

Abstract

For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical particles, we exploit the fact that this method separates the problem of the potential, dealt with by the Feynman-Kac functional, from the process which gives sample paths of a non-interacting system. For motion in 1 dimension, we emphasize that the permutation symmetry of the identical particles completely determines the domain of Brownian motion and the appropriate boundary conditions: absorption for fermions, reflection for bosons. Further analysis of the sample paths for motion in 3 dimensions allows us to decompose these paths into a superposition of 1-dimensional sample paths. This reduction expresses the propagator (and consequently the energy and other thermodynamical quantities) in terms of well-behaved 1-dimensional fermion and boson diffusion processes and the Feynman-Kac functional.

13 pages, REVTEX, no figures. Added: Erratum on orthogonality relations Eq. (4.16)

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