00-521 Vladimir GEORGESCU, Andrei IFTIMOVICI

$C^*$-Algebras of Energy Observables: I. General Theory and Bumps Algebras (704K, Postscript) Dec 31, 00

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Abstract. To a quantum system subject to a qualitatively specified interaction we associate a $C^*$-algebra acting on the state space of the system: the $C^*$-algebra generated by the operators which can be interpreted as hamiltonians of the system. Our purpose is to show the relevance of this algebra in the study of the spectral properties of the hamiltonians and to give concrete methods of construction of such algebras. The main tool we use is the crossed product of $C^*$-algebras by actions of groups. Applications include systems with anisotropic behaviour at infinity, generalized $N$-body problems, quantum field models. We study in detail the algebra associated to a system subject to a Klaus type interaction (infinitely many bumps).

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