Quantum fields and Poisson processes: Interaction of a cut-off boson field with a quantum particle (Q1063345)

A model of quantum particle interacting with a boson field on a lattice with energy cut-off is considered. The solution of the associated Schrödinger equation is written as an expectation value with respect to a jump process. This process has a simple physical meaning as it is defined by a Poisson measure counting the jumps of occupation numbers for each field mode. Moreover, it allows to show the existence and to write in closed form the solution of a problem involving an unbounded interaction.