Hans-Otto Georgii, Roderich Tumulka
Global Existence of Bell's Time-Inhomogeneous Jump Process
for Lattice Quantum Field Theory
(50K, LaTeX)

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.