Related papers: Deformation Quantization of Kahler Manifolds

We give a classification of polarized deformation quantizations on a symplectic manifold with a (complex) polarization. Also, we establish a formula which relates the characteristic class of a polarized deformation quantization to its…

In this paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is K\"ahler equipped with transversal complex polarizations $T^{1, 0}X,…

We describe the deformed E.T. quantization rules for kappa-deformed free quantum fields, and relate these rules with the kappa-deformed algebra of field oscillators.

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the…

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…

We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a K\"ahler manifold M. Unlike C_1 and C_2, this operator can not be expressed in terms of the K\"ahler-Poisson tensor on…

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the…

We adapt to the case of deformation quantization modules a formula of V. Lunts who calculates the trace of a kernel acting on Hochschild homology.

In this paper we provide a quantization via formality of Poisson actions of a triangular Lie algebra $(\mathfrak g,r)$ on a smooth manifold $M$. Using the formality of polydifferential operators on Lie algebroids we obtain a deformation…

Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…

This work considers a formal deformation of the quantum disc (it is developed via an application of the Berezin method) and presents an explicit formula for this deformation.

We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…

We extend Fedosov deformation quantization to general contact manifolds. Unlike the case of symplectic manifolds, not every classical observable on a contact manifold is generally quantized. On examination of possible obstructions to…

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

We show that the number of equivariant deformation classes of real structures in a given deformation class of compact hyperkahler manifolds is finite.

For every compact K\"ahler manifold $X$ of algebraic dimension $a(X) = \dim X - 1$, we prove that $X$ has arbitrarily small deformations to some projective manifolds.

In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on…

We study the singularity of Quillen metrics for one-parameter degenerations of compact Kaehler manifolds.

This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential…