Related papers: Deformation Quantization of Kahler Manifolds

We show that two approaches to equivariant strict deformation quantization of C*-algebras by actions of negatively curved Kahlerian Lie groups, one based on oscillatory integrals and the other on quantizations maps defined by dual…

On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…

We provide infinitely many examples of pairs of diffeomorphic, non simply connected K\" ahler manifolds of complex dimension three with different Kodaira dimensions. Also, in any possible Kodaira dimension we find infinitely many pairs of…

We prove estimates for the sectional curvature of hyperkaehler quotients and give applications to moduli spaces of solutions to Nahm's equations and Hitchin's equations.

We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…

With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.

In this note, we show that the obstruction classes of deforming vector forms on a compact K\"ahler manifold is annihilated by cohomology classes.

For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$…

Using the classification of formal deformation quantizations, and the formal, algebraic index theorem, I give a simple proof as to which formal deformation quantization (modulo isomorphism) is derived from a given geometric quantization.

In this paper, we study the deformation limit of compact Kahler manifolds. We show that the limit to be a manifold in the Fujiki class C is equivalent to the finiteness of the upper volume. We also prove the Streets-Tian conjecture for a…

An algebraic deformation theory of dialgebra morphisms is obtained.

We give an answer to the Nielsen realization problem for hyper-K\"ahler manifolds in terms of the same invariant used for K3 surfaces. We determine that, for some of the known deformation types, the representation of the mapping class group…

Motivated by the problem of transverse deformation quantization of foliated manifolds, we describe a quantization of Dirac structures (more precisely, of those that are formal deformations of regular ones) to stacks of algebroids in the…

Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach…

A proposed definition is given for the quantization of a Poisson algebra, taking the quantum product to be a geodesic on the manifold of associative products.

The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) K\"ahler manifold. The deformation quantisation for such systems is scetched resulting in the Wick-type symbols for the…

We propose that under certain conditions heterotic string compactifications on half-flat and nearly-Kahler manifolds are equivalent. Based on this correspondence we argue that the moduli space of the nearly-Kahler manifolds under discussion…

We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurgent operators with algebraic singularities. This algebra…

We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a…

A complete description of the deformation classes of real ruled manifolds is given. In particular, we prove that once the complex deformation class is fixed, the real deformation class is prescribed by the topology of the real structure.