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We present a simple derivation of a Feynman-Kac type formula to studyfermionic systems. In this approach the real time or the imaginary timedynamics is expressed in terms of the evolution of a collection of Poissonprocesses. A computer implementation of this formula leads to a family ofalgorithms parametrized by the values of the jump rates of the Poissonprocesses. From these an optimal algorithm can be chosen which coincides withthe Green Function Monte Carlo method in the limit when the latter becomesexact.Comment: 4 pages, 1 PostScript figure, REVTe

An exact representation of the fermion dynamics in terms of Poisson processes and its connection with Monte Carlo algorithms