| [1] |
G F De Angelis, G Jona-Lasinio, and V Sidoravicius.
Berezin integrals and poisson processes.
J. Phys. A: Math. Gen., 31:289-308, 1998. BibTeX entry, PDF
We show that the calculation of Berezin integrals over anticommuting variables can be reduced to the evaluation of expectations of functionals of Poisson processes via an appropriate Feynman Kac formula. In this way the tools of ordinary analysis can be applied to Berezin integrals and, as an example, we prove a simple upper bound. Possible applications of our results are briefly mentioned.
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| [2] |
M. Beccaria, C. Presilla, G. F. De Angelis, and G. Jona-Lasinio.
An exact representation of the fermion dynamics in terms of poisson
processes and its connection with monte carlo algorithms.
Europhys. Lett., 48(3):243-249, November 1999. BibTeX entry, PDF
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. 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 method in the limit when the latter becomes exact.
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