Path-integral approach to a finite many-body problem

Jean-Paul Blaizot, Henri Orland

A. Chouchaoui

Dinkar C. Khandekar, S. V. Lawande

A one dimensional three body problem is treated by the path integral approach of Feynman. When expressed in suitable coordinates, it is possible to extract the symmetry from the path integral of the problem. The resulting propagator is evaluated in a closed analytical form.

Ricardo A. Broglia

John W. Negele, Henri Orland

This chapter describes the range of techniques available for the stochastic evaluation of path integrals and how this flexibility may be effectively exploited to incorporate one's understanding of the underlying physics in the method. It provides precise calculations of physical observables which are exact within controllable systematic and stochastic sampling errors. A special problem frequently arising in stochastic solutions of many-body problems is sampling of the inverse of a matrix. The principal intellectual challenge is to exploit the freedom and to utilize physical insight to incorporate as much of the essential physics of the problem as possible into the stochastic algorithm. It is natural to ask whether any of the functional integral representations of the many-body evolution operator using fields are preferable to the particle coordinate path integral for stochastic calculations. One alternative to evaluate the evolution operator for spin systems is to use the Trotter formula for other path integrals.

João da Providência