 0199 Vladimir GEORGESCU, Andrei IFTIMOVICI
 C*Algebras of Energy Observables: II. Graded Symplectic Algebras and Magnetic Hamiltonians
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Mar 12, 01

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Abstract. To each symplectic space $\Xi$ we associate a $C^*$algebra
${\mathcal C}^\Xi$ graded by the lattice of all linear subspaces of
$\Xi$. The hamiltonians of $N$body systems in constant magnetic
fields are affiliated to $C^*$subalgebras of ${\mathcal C}^\Xi$ for
certain choices of $\Xi$, and this allows one to study their spectral
properties. The algebra generated by the hamiltonians
corresponding to a fixed magnetic field can also be described as
the crossed product of an abelian algebra (of ``classical
potentials'') by the action of a nonabelian group. This point of view
is generalized to the case of nonconstant magnetic fields.
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