Communications in Mathematical Physics

, Volume 228, Issue 3, pp 519–560

Crossed Products of C*-Algebras and Spectral Analysis of Quantum Hamiltonians

  • Vladimir Georgescu
  • Andrei Iftimovici

DOI: 10.1007/s002200200669

Cite this article as:
Georgescu, V. & Iftimovici, A. Commun. Math. Phys. (2002) 228: 519. doi:10.1007/s002200200669

Abstract:

We study spectral properties of a hamiltonian by analyzing the structure of certain C*-algebras to which it is affiliated. The main tool we use for the construction of these algebras is the crossed product of abelian C*-algebras (generated by the classical potentials) by actions of groups. We show how to compute the quotient of such a crossed product with respect to the ideal of compact operators and how to use the resulting information in order to get spectral properties of the hamiltonians. This scheme provides a unified approach to the study of hamiltonians of anisotropic and many-body systems (including quantum fields).

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Vladimir Georgescu
    • 1
  • Andrei Iftimovici
    • 2
  1. 1.CNRS. E-mail: Vladimir.Georgescu@math.u-cergy.frFR
  2. 2.Department of Mathematics, University of Cergy-Pontoise, 2, avenue Adolphe Chauvin,¶95302 Cergy-Pontoise Cedex, France. E-mail: Andrei.Iftimovici@math.u-cergy.frFR