On the Spectrum of a Model Operator in Fock Space

TL;DR

This paper analyzes a model operator related to a four-particle interaction system in Fock space, describing its essential spectrum, proving the HWZ theorem, and providing variational principles for spectral boundaries and eigenvalues.

Contribution

It introduces a detailed spectral analysis of a complex four-particle interaction operator, including the HWZ theorem and variational principles, advancing understanding of such quantum systems.

Findings

Describes the essential spectrum via channel operators

Proves the HWZ theorem for the model operator

Provides variational principles for spectral boundaries

Abstract

A model operator $H$ associated to a system describing four particles in interaction, without conservation of the number of particles, is considered. We describe the essential spectrum of $H$ by the spectrum of the channel operators and prove the Hunziker-van Winter-Zhislin (HWZ) theorem for the operator $H.$ We also give some variational principles for boundaries of the essential spectrum and interior eigenvalues.