Quantum Hamiltonians and Stochastic Jumps

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  • 11 March 2003
Abstract
With many Hamiltonians one can naturally associate a |Psi|^2 distributed Markov process. For nonrelativistic quantum mechanics, it is in fact a deterministic process known as Bohmian mechanics. The analogue for the Hamiltonian of a quantum field theory is typically a jump process on the configuration space of a variable number of particles. We develop here the general theory of these processes, applicable to every quantum field theory, thereby generalizing previous work of John S. Bell [Phys. Rep. 137, 49 (1986)] and of ourselves [quant-ph/0208072]. In particular, we show how to obtain the process from processes corresponding to the free and interaction Hamiltonian alone, and the free process from the one-particle process. We introduce a formula for the jump rates as depending on the interaction Hamiltonian, and establish a condition for finiteness of the rates.

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