  Recently, there has been progress in developing interior-boundary conditions
(IBCs) as a technique of avoiding the problem of ultraviolet divergence in
non-relativistic quantum field theories while treating space as a continuum and
electrons as point particles. An IBC can be expressed in the particle-position
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 $|\psi|^2$ distribution, time reversal
symmetry, and the Markov property. The process is closely related to processes
known as Bell-type quantum field theories.
