An exact representation of the fermion dynamics in terms of Poisson processes

Beccaria, Matteo; Presilla, Carlo; De Angelis, Gian Fabrizio; Jona-Lasinio, Giovanni

An exact representation of the fermion dynamics in terms of Poisson processes

Authors

Beccaria, Matteo

Presilla, Carlo

De Angelis, Gian Fabrizio

Jona-Lasinio, Giovanni

Description

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo (GFMC) method in the limit when the latter becomes exact.
3 pages, LATTICE99 submission