Let Gamma be a discrete subgroup PSL(2,R). We describe a class of completely positive maps related to the von Neumann algebras in the Berezin's equivariant deformation quantization of the upper half plane, module the discrete subgroup Gamma. When Gamma is PSL(2, Z) we find a non-trivial obstruction for the existence of a one parameter family of isomorphisms, having a generator that preserves a certain differential structure, between the von Neumann algebras in the deformation.
Radulescu, F. (1996). Quantum dynamics and Berezin's deformation quantization. In S. Doplicher, R. Longo, J.E. Roberts, L. Zsido (a cura di), Conference on Operator Algebras and Quantum Field Theory, ACAD NAZL LINCEI, ROME, ITALY (pp. 383-389). Roma : INTERNATIONAL PRESS INC BOSTON, PO BOX 2872, CAMBRIDGE, MA 02238-2872 USA.
Quantum dynamics and Berezin's deformation quantization
RADULESCU, FLORIN
1996-01-01
Abstract
Let Gamma be a discrete subgroup PSL(2,R). We describe a class of completely positive maps related to the von Neumann algebras in the Berezin's equivariant deformation quantization of the upper half plane, module the discrete subgroup Gamma. When Gamma is PSL(2, Z) we find a non-trivial obstruction for the existence of a one parameter family of isomorphisms, having a generator that preserves a certain differential structure, between the von Neumann algebras in the deformation.| File | Dimensione | Formato | |
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