A method for constructing all admissible unitary non-equivalent Wigner quasiprobability distributions providing the Stratonovic-h-Weyl correspondence an arbitrary N-level quantum system is proposed. The based on reformulation of Stratonovich–Weyl in form algebraic “master equations” spectrum kernel. later implements a map between operators Hilbert space and functions phase identified by complex...

We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasiisomorphism. The counterpart on star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated. Mathematics Subject Classification (2000) : 16S80, 53D17, 53D55, 58A50.

The third author recently proved that the Shoikhet–Dolgushev L∞-morphism from Hochschild chains of the algebra of smooth functions on manifold to differential forms extends to cyclic chains. Localization at a solution of the Maurer–Cartan equation gives an isomorphism, which we call character map, from the periodic cyclic homology of a formal associative deformation of the algebra of functions ...

An adaption of Rieeel's notion of`strict deformation quantization' is applied to a particle moving on an arbitrary Riemannian manifold Q in an external gauge eld, that is, a connection on a principal H-bundle P over Q. Hence the Poisson algebra A 0 = C 0 ((T P)=H) is deformed into the C-algebra A = K(L 2 (P)) H of H-invariant compact operators on L 2 (P), which is isomorphic to K(L 2 (Q)) C (H)...

Let XR be a (generalized) flag manifold of a non-compact real semisimple Lie group GR, where XR and GR have complexifications X and G. We investigate the problem of constructing a graded star product on Pol(T ∗XR) which corresponds to a GR-equivariant quantization of symbols into smooth differential operators acting on half-densities on XR. We show that any solution is algebraic in that it rest...

A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic c...

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.

It is shown that a quantum groupoid (or a QUE algebroid, i.e., deformation of the universal enveloping algebra of a Lie algebroid) naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization problem, is raised, and it is proved for all regular triangular Lie bialgebroids. For a Poisson manifold P , the existence of a star-product is shown to be ...

This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We als...