Duerr, Detlef; Goldstein, Sheldon; Teufel, Stefan; Tumulka, Roderich; Zanghi, Nino
(2020):
Bohmian Trajectories for Hamiltonians with InteriorBoundary Conditions.
In: Journal of Statistical Physics, Vol. 180: pp. 3473

Full text not available from 'Open Access LMU'.
Abstract
Recently, there has been progress in developing interiorboundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in nonrelativistic quantum field theories while treating space as a continuum and electrons as point particles. An IBC can be expressed in the particleposition representation of a Fock vector psi as a condition on the values of psi on the set of collision configurations, and the corresponding Hamiltonian is defined on a domain of vectors satisfying this condition. We describe here how Bohmian mechanics can be extended to this type of Hamiltonian. In fact, part of the development of IBCs was inspired by the Bohmian picture. Particle creation and annihilation correspond to jumps in configuration space;the annihilation is deterministic and occurs when two particles (of the appropriate species) meet, whereas the creation is stochastic and occurs at a rate dictated by the demand for the equivariance of the vertical bar psi vertical bar(2) distribution, time reversal symmetry, and the Markov property. The process is closely related to processes known as Belltype quantum field theories.