Essential spectrum of a fermionic quantum field model

Abstract

An interaction system of a fermionic quantum field is considered. The state space is defined by a tensor product space of a fermion Fock space and a Hilbert space. It is assumed that the total Hamiltonian is a self-adjoint operator on the state space and bounded from below. Then it is proven that a subset of real numbers is the essential spectrum of the total Hamiltonian. It is applied to a Yukawa interaction system, which is a system of a Dirac field coupled to a Klein–Gordon, and the HVZ theorem is obtained.