Global Existence of Bell's Time-Inhomogeneous Jump Process for Lattice Quantum Field Theory

#### H.-O. Georgii, R. Tumulka

2005, v.11, №1, 1-18

ABSTRACT

We consider the time-inhomogeneous Markovian jump process introduced by John S. Bell [J.S. Bell, Beables for quantum field theory, Phys. Rep., 1986, v.137, 49-54] 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.

Keywords: Markov jump processes,non-explosion,time-dependentjump rates,equi-variant distributions,Bell's process,lattice quantum field theory