Related papers: Quantization of K\"ahler manifolds

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical…

Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as…

To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to the formal neighborhood of the diagonal of the product M x M~,…

This paper is the continuation of arXiv:0802.1245. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and…

As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of…

In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…

A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…

Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic…

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…

We survey some recent developments in the study of canonical K\"{a}hler metrics on algebraic varieties and their relation with stability in algebraic geometry.

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…

In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact K\"ahler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact…

Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…

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 explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…

Recent developments of Batalin-Vilkovisky (BV) formalism and related geometry are reviewed. Mathematical structures of BV formalism are summarized as a Q-manifold and a QP-manifold. Lie algebras, Lie algebroids and other higher algebroids…

We demonstrate the relation between the isospectral deformation and Rieffel's deformation quantization by the action of $\mathbb{R}^d$.

We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them in a wider context.

Finsler and Lagrange spaces can be equivalently represented as almost Kahler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to…