Hilbert C*-modules and spectral analysis of many-body systems

2008/06/04 by Mondher Damak, Damak, Mondher, Vladimir Georgescu +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #46L60 #47L90 #81Q10 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Lanthanide and Transition Metal Complexes #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.OA #msc:46L60 #msc:47L90 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.0806.0827

arxiv created 2008/06/04 · openalex publication_date 2008/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spectral properties of a class of many channel Hamiltonians which contains those of systems of particles interacting through k-body and field type forces which do not preserve the number of particles. Our results concern the essential spectrum, the Mourre estimate, and the absence of singular continuous spectrum. The appropriate formalism involves graded C*-algebras and Hilbert C*-modules as basic tools.

Citations

• K-theory of C*—Algebras in solid state physics

Cited by

• On the spectral analysis of many-body systems

Related

• On the spectral analysis of many-body systems
• A Unified Algebraic Approach to Few and Many-Body Hamiltonians having Linear Spectra
• Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanics
• On the Spectral Analysis of Quantum Field Hamiltonians
• On the Spectrum of a Model Operator in Fock Space