Related papers: Deformation quantization of compact Kaehler manifo…
In this thesis, we introduce complex manifolds with local spectral gaps and study their asymptotic behavior using the scaling method. With these asymptotics, we obtain an asymptotic expansion for the Bergman kernel of a Hermitian…
In this note, we study Schwarz's conjecture on application of Q-algebras to strict quantization. We prove that in the case of a torus with a constant Poisson structure, Schwarz's formalism gives the same star product as Rieffel…
Over the last 25 years, the notion of "fuzzy spaces" has become ubiquitous in the high-energy physics literature. These are finite dimensional noncommutative approximations of the algebra of functions on a classical space. The most well…
In this paper we establish a notion of deformation quantization of a surjective submersion which is specialized further to the case of a principal fibre bundle: the functions on the total space are deformed into a right module for the star…
This paper develops an approach to categorical deformation quantization via factorization homology. We show that a quantization of the local coefficients for factorization homology is equivalent to consistent quantizations of its value on…
Deformation theory refers to an apparatus in many parts of math and physics for going from an infinitesimal (= first order) deformation to a full deformation, either formal or convergent appropriately. If the algebra being deformed is that…
We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string…
Given a regular weight $\omega$ and a positive Borel measure $\mu$ on the unit disc $\mathbb{D}$, the Toeplitz operator associated with $\mu$ is $$ \mathcal{T}_\mu(f)(z)=\int_{\mathbb{D}} f(\zeta)\bar{B_z^\omega(\zeta)}\,d\mu(\zeta), $$…
We define a normalized Weyl-type $\star$-product on general K\"{a}hler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order…
We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein…
In their physical proposal for quantization [20], Gukov-Witten suggested that, given a symplectic manifold $M$ with a complexification $X$, the A-model morphism spaces $\operatorname{Hom}(\mathcal{B}_{\operatorname{cc}},…
We define a natural class of star products: those which are given by a series of bidifferential operators which at order $k$ in the deformation parameter have at most $k$ derivatives in each argument. We show that any such star product on a…
The aim of this proceeding is to give a basic introduction to Deformation Quantization (DQ) to physicists. We compare DQ to canonical quantization and path integral methods. It is described how certain issues such as the roles of…
We characterize boundedness and compactness of Toeplitz operators on large vector-valued Fock spaces with Dall'Ara's weights [Adv.\ Math., 285 (2015) 1706--1740] in terms of generalized Berezin transforms, averaging functions, and Carleson…
We generalize some earlier results on a Berezin-Toeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and…
I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a…
We define and study coherent states, a Berezin-Toeplitz quantization and covariant symbols on the product between a connected simply connected nilpotent Lie group and the dual of its Lie algebra. The starting point is a Weyl system…
We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schr\"{o}dinger picture by a star-product induced by a modified "Poisson…
In this article we characterize the boundedness and compactness of a Toeplitz-type operator on weighted Bergman spaces satisfying the so-called Bekolle-Bonami condition in terms of the Berezin transform.
In this paper we give a construction of Fedosov quantization incorporating the odd variables and an analogous formula to Getzler's pseudodifferential calculus composition formula is obtained. A Fedosov type connection is constructed on the…