On the Spectral Analysis of Quantum Field Hamiltonians

TL;DR

This paper develops a spectral analysis framework for quantum field Hamiltonians with positive mass by defining specific C*-algebras, analyzing their quotients, and deriving spectral properties including the essential spectrum and Mourre estimates.

Contribution

It introduces a new algebraic approach to study the spectral properties of quantum field Hamiltonians with positive mass.

Findings

Computed the essential spectrum of the Hamiltonians.

Provided a systematic method for establishing Mourre estimates.

Linked algebraic structures to spectral properties in quantum field models.

Abstract

We define C*-algebras on a Fock space such that the Hamiltonians of quantum field models with positive mass are affiliated to them. We describe the quotient of such algebras with respect to the ideal of compact operators and deduce consequences in the spectral theory of these Hamiltonians: we compute their essential spectrum and give a systematic procedure for proving the Mourre estimate.