Quantum Hamiltonians and Stochastic Jumps

Details Quantum Hamiltonians and Stochastic Jumps Quantum Hamiltonians and Stochastic Jumps

2003-03-11

arxiv.org/abs/quant-ph/0303056v3

Communications in Mathematical Physics 254:129-166 (2005)

Physics

Quantum Physics

43 pages LaTeX, no figures. The old version v2 has been divided in two parts, the first of which is the present version v3, an

Scientific paper

10.1007/s00220-004-1242-0

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 define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [Phys. Rep. 137, 49 (1986)] and of ourselves [J. Phys. A: Math. Gen. 36, 4143 (2003)]. 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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