We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time-zero fields which satisfy the canonical commutation relations. We show that the model has a ground state for all values of the coupling constant even in the case where no infrared cutoff is made. The non-Fock representation used is inequivalent to the Fock one if no infrared cutoff is made.
We study rigorously the problem of the lamb shift and the spontaneous emission of light in a framework of nonrelativistic quantum electrodynamics by using an exactly soluble model of a harmonic oscillator atom interacting with a quantized electromagnetic field. We show that, under the perturbation of the electromagnetic field, all the point spectra corresponding to the excited states of the unperturbed atom disappear. This means that the ‘‘energy level shifts’’ (Lamb shifts) of the excited states of the atom cannot be described simply in terms of shifts of point spectra. Then, we give a rigorous mathematical meaning to both formal perturbation theories for the ‘‘energy level shifts’’ and for the transitions of the excited states due to the spontaneous emission of light, showing that the ‘‘energy level shifts’’ and the ‘‘decay probabilities’’ of the excited states of the atom are characterized in terms of the resonance pole of the S-matrix for the photon scattering by the atom. We also discuss broken symmetry aspects and infinite mass-renormalization of the model.
A class of models of quantized, massless Bose fields, called the generalized spinboson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455 503) is considered. Theorems on the absence of ground states and the other eigenvectors of the model without infrared cutoff (but with ultraviolet cutoff ) are established with conditions in terms of correlation functions for some operators.
Academic PressKey Words: massless quantum field; Fock space; infrared problem; generalized spin-boson model; ground state; eigenvector; correlation function; particle-field interaction; spin-boson model; Pauli Fierz model. Article ID jfan.1999.3472, available online at http:ÂÂwww.idealibrary.com on 470
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.