This monograph offers a state-of-the-art mathematical account of functional integration
methods in the context of self-adjoint operators and semigroups using the concepts and …

We consider a charged particle, spin 12, with relativistic kinetic energy and minimally
coupled to the quantized Maxwell field. Since the total momentum is conserved, the …

A Feynman–Kac-type formula for a Lévy and an infinite-dimensional Gaussian random
process associated with a quantized radiation field is derived. In particular, a functional …

A translation invariant Hamiltonian H of non-relativistic quantum electrodynamics is studied.
This Hamiltonian is decomposed with respect to the total momentum PT: where the self …

We mathematically study the infrared catastrophe for the Hamiltonian of Nelson's model
when it has the external potential in a general class. For the model, we prove the pull …

In this paper, we consider the spectrum of a model in quantum electrodynamics with a
spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint;(2) under the infrared …

We consider moving atoms and ions in R3 interacting with the quantized electromagnetic
field. Because of the translation invariance we consider the reduced Hamiltonian associated …

This book provides self-contained proofs of the existence of ground states of several
interaction models in quantum field theory. Interaction models discussed here include the …

In this paper we consider generalized spin-boson models with singular perturbations. It is
proven that under the infrared regularity condition Hamiltonians have the unique ground …

We consider a Hamiltonian with cutoffs describing the weak decay of spin 1 massive bosons
into the full family of leptons. The Hamiltonian is a self‐adjoint operator in an appropriate …