Essential spectrum of a fermionic quantum field model

TL;DR

This paper analyzes the essential spectrum of a fermionic quantum field model, establishing spectral properties of the Hamiltonian and applying the results to Dirac and Klein-Gordon field systems.

Contribution

It proves the essential spectrum characterization for a fermionic quantum field Hamiltonian and extends the HVZ theorem to this system.

Findings

Identifies the essential spectrum of the fermionic quantum field Hamiltonian.

Establishes the self-adjointness and boundedness from below of the Hamiltonian.

Derives the HVZ theorem for the coupled Dirac and Klein-Gordon fields.

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 the system of a Dirac field coupled to a Klein-Gordon field. Then the HVZ theorem for the system is obtained.