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

Mondher Damak (1) , Vladimir Georgescu (2)

1 Université de Sfax - University of Sfax
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Algèbres d'opérateurs [math.OA]

Mondher Damak, Vladimir Georgescu. Hilbert C*-modules and spectral analysis of many-body systems. 2008. ⟨hal-00285199⟩