04-11 Hans-Otto Georgii, Roderich Tumulka

Global Existence of Bell's Time-Inhomogeneous Jump Process for Lattice Quantum Field Theory (50K, LaTeX) Jan 20, 04

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Abstract. We consider the time-inhomogeneous Markovian jump process introduced by John S. Bell [Phys.Rep.137, 49 (1986)] for a lattice quantum field theory, which runs on the associated configuration space. Its jump rates, tailored to give the process the quantum distribution $|\Psi_t|^2$ at all times t, typically exhibit singularities. We establish the existence of a unique such process for all times, under suitable assumptions on the Hamiltonian or the initial state vector $\Psi_0$. The proof of non-explosion takes advantage of the special role of the $|\Psi_t|^2$ distribution.

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