Vladimir GEORGESCU, Andrei IFTIMOVICI
C*-Algebras of Energy Observables: II. Graded Symplectic Algebras and Magnetic Hamiltonians
(484K, Postscript)
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 non-abelian group. This point of view
is generalized to the case of non-constant magnetic fields.