- 00-521 Vladimir GEORGESCU, Andrei IFTIMOVICI
- $C^*$-Algebras of Energy Observables:
I. General Theory and Bumps Algebras
Dec 31, 00
(auto. generated ps),
of related papers
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).