Crossed Products of C*-Algebras and Spectral Analysis of Quantum Hamiltonians |
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Authors: | Vladimir Georgescu Andrei Iftimovici |
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Affiliation: | 1.CNRS. E-mail: Vladimir.Georgescu@math.u-cergy.fr,FR;2.Department of Mathematics, University of Cergy-Pontoise, 2, avenue Adolphe Chauvin,?95302 Cergy-Pontoise Cedex, France. E-mail: Andrei.Iftimovici@math.u-cergy.fr,FR |
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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). Received: 5 November 2001 / Accepted: 10 March 2002 |
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