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

Abstract

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.

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

References in corpus (4)

• Bohmian Mechanics and Quantum Field Theory
• Quantum Hamiltonians and Stochastic Jumps
• Purifying Quantum States: Quantum and Classical Algorithms
• The continuum limit of the Bell model

Cited by in corpus (4)

• Simple Proof for Global Existence of Bohmian Trajectories
• Quantum Hamiltonians and Stochastic Jumps
• The Analogue of Bohm-Bell Processes on a Graph
• Bell's Jump Process in Discrete Time