Some Jump Processes in Quantum Field Theory

Details Some Jump Processes in Quantum Field Theory Some Jump Processes in Quantum Field Theory

2003-12-17

arxiv.org/abs/math/0312326v2

P. 55-73 in J.-D. Deuschel, A. Greven (editors): Interacting Stochastic Systems. Berlin: Springer-Verlag (2005)

Mathematics

Probability

18 pages LaTeX, no figures; written for the proceedings of the DFG Priority Program "Interacting Stochastic Systems of High Co

Scientific paper

A jump process for the positions of interacting quantum particles on a lattice, with time-dependent transition rates governed by the state vector, was first considered by J.S. Bell. We review this process and its continuum variants involving ``minimal'' jump rates, describing particles as they get created, move, and get annihilated. In particular, we sketch a recent proof of global existence of Bell's process. As an outlook, we suggest how methods of this proof could be applied to similar global existence questions, and underline the particular usefulness of minimal jump rates on manifolds with boundaries.

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