量子哈密顿量与随机跳跃
Quantum Hamiltonians and Stochastic Jumps
摘要：
对于许多哈密顿量，人们可以很自然地将其与一个|Psi| ^2分布马尔可夫过程联系起来。对于非相对论性的量子力学，这个过程实际上是决定性的，被称为玻姆力学。对于量子场论的哈密顿量，它是一个典型的变量粒子位形空间上的跳跃过程。我们为正则化的量子场论定义了这些过程，从而推广了John S. Bell [Phys.Rep.137，49（1986）]和我们自己[J.Phys.A：Math.Gen.36，4143（2003）]。我们引入了一个用相互作用哈密顿量表示跳跃率的公式，并建立了跳跃率有限的条件。
英文摘要：
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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