Related papers: Universal star products
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
We give an elementary proof of the result by Leichtnam, Tang, and Weinstein that there exists a deformation quantization with separation of variables on a complex manifold endowed with a Kaehler-Poisson structure vanishing on a Levi…
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 deal with smooth real manifolds as well as complex analytic manifolds as well. It is well known that the concept of star product is powerful enough to produce all Poisson structures on real manifolds. According to [BdM] it is not known…
It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that noncommutative gauge theories on more…
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…
In this paper we provide an explicit construction of star products on U(g)-module algebras by using the Fedosov approach. This construction allows us to give a constructive proof to Drinfel'd theorem and to obtain a concrete formula for…
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and…
We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…
We give a complete identification of the deformation quantization which was obtained from the Berezin-Toeplitz quantization on an arbitrary compact Kaehler manifold. The deformation quantization with the opposite star-product proves to be a…
This talk reports on results on the deformation quantization (star products) and on approximative operator representations for quantizable compact K"ahler manifolds obtained via Berezin-Toeplitz operators. After choosing a holomorphic…
We obtain deformations of a crossed product of a polynomial algebra with a group, under some conditions, from universal deformation formulas. We show that the resulting deformations are nontrivial by a comparison with Hochschild cohomology.…
The deformation star product of smooth functions on the momentum phase space of covariant (polysymplectic) Hamiltonian field theory is introduced.
The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent…
Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…
We develop the theory of $\hbar$-vertex algebras, algebraic structures closely related to vertex algebras but with a deformed translation covariance axiom. We establish their structure theory, including analogues of Goddard's Uniqueness…
Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…
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…
A compactification over $\overline{M}_g$ of $M_{g,n}$ is obtained by considering the relative Fulton-MacPherson configuration space of the universal curve. The resulting compactification differs from the Deligne-Mumford space…
We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from realizations are presented, as well as their…