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

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

2003-12-15

arxiv.org/abs/math/0312294v2

Markov Processes and Related Fields 11, 1-18 (2005)

Mathematics

Probability

16 pages LaTeX, no figures; v2: references added, minor extension of the introduction

Scientific paper

We consider the time-inhomogeneous Markovian jump process introduced by John S. Bell [Phys.Rep. 137, 49] 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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