On the Absence of Eigenvectors of Hamiltonians in a Class of Massless Quantum Field Models without Infrared Cutoff

A class of models of quantized, massless Bose fields, called the generalized spin-boson 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.