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).
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Received: 5 November 2001 / Accepted: 10 March 2002
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Georgescu, V., Iftimovici, A. Crossed Products of C*-Algebras and Spectral Analysis of Quantum Hamiltonians. Commun. Math. Phys. 228, 519–560 (2002). https://doi.org/10.1007/s002200200669
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DOI: https://doi.org/10.1007/s002200200669