Quantum Hamiltonians and Stochastic Jumps

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  • 12 October 2003
Abstract
With many Hamiltonians one can naturally associate a |Psi|^2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it 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 regularized quantum field theories, thereby generalizing previous work of John S. Bell [Phys. Rep. 137, 49] and of ourselves [quant-ph/0208072]. In particular, we show how to obtain the process from processes corresponding to the free and interaction Hamiltonians alone, and the free process from the one-particle process. We introduce a formula expressing the jump rates in terms of the interaction Hamiltonian, and establish a condition for finiteness of the rates.

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