Quantification formelle des variétés de Poisson
Quantization and Morita equivalence for constant Dirac structures on tori
We define a -algebraic quantization of constant Dirac structures on tori and prove that -equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.
Quantization of pencils with a gl-type Poisson center and braided geometry
We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...
Quantization of Poisson structures on .
Quantization of the cotangent bundle via the tangent groupoid
Quantization of the orientation preserving automorphisms of the torus
Quantizations and symbolic calculus over the -adic numbers
We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the -adic numbers. We apply this theory to the study of elliptic operators over the -adic numbers and determine their asymptotic spectral behavior.
Quantum ergodicity of C*-dynamical systems
Quantum mechanics and nonabelian theta functions for the gauge group SU(2)
We propose a direction of study of nonabelian theta functions by establishing an analogy between the Weyl quantization of a one-dimensional particle and the metaplectic representation on the one hand, and the quantization of the moduli space of flat connections on a surface and the representation of the mapping class group on the space of nonabelian theta functions on the other. We exemplify this with the cases of classical theta functions and of the nonabelian theta functions for the gauge group...
Quantum structures in Galilei general relativity