Essential spectrum of a fermionic quantum field model
Functional Analysis
2014-01-16 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1211.4965,
title = {Essential spectrum of a fermionic quantum field model},
author = {Toshimitsu Takaesu},
journal= {arXiv preprint arXiv:1211.4965},
year = {2014}
}