Essential Spectrum of a Self-Adjoint Operator on an Abstract Hilbert Space of Fock Type and Applications to Quantum Field Hamiltonians

We establish general theorems on locating the essential spectrum of a self-ad- joint operator of the form AmIqImdG S.qHI on the tensor product Hm Fb K. of a Hilbert space H and the abstract Boson Fock space Fb K. over a Hilbert space K, where A is a self-adjoint operator on H bounded from below, dG S. is the second quantization of a nonnegative self-adjoint operator S on K, and HI is a symmetric operator on HmFb K.. We then apply the theorems to the generalized spin-boson model by A. Arai and M. Hirokawa 1997, J. Funct. Anal. 151, 455]503. and a general class of models of quantum particles coupled to a Bose field including the Pauli]Fierz model in nonrelativistic quantum electrody - namics.