Related papers: On a connection used in deformation quantization

A geometric derivation of $W_\infty$ Gravity based on Fedosov's deformation quantization of symplectic manifolds is presented. To lowest order in Planck's constant it agrees with Hull's geometric formulation of classical nonchiral…

We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the…

In a seminal paper Drinfel'd explained how to associate to every classical r-matrix for a Lie algebra $\lie g$ a twisting element based on $\mathcal{U}(\lie g)[[\hbar]]$, or equivalently a left invariant star product of the corresponding…

We make some observations about Rosenberg's Levi-Civita connections on noncommutative tori, noting the non-uniqueness of torsion-free metric-compatible connections without prescribed connection operator for the inner *-derivations, the…

This thesis contains an introduction to the method of average in Finsler geometry. The method is applied to Berwald spaces, obtaining geodesic rigidity conditions. We prove that the Levi-Civita connection of any Riemannian metric affine…

We reconstruct a Riemannian manifold and a Hermitian vector bundle with compatible connection from the hyperbolic Dirichlet-to-Neumann operator associated with the wave equation of the connection Laplacian. The boundary data is local and…

We show that for every vector bundle E over any given symplectic manifold M there exists an explicitly given super-Poisson bracket on the space of sections of the dual Grassmann bundle associated to E built out of symplectic structure of M,…

We give simple explicit formulas for deformation quantization of Poisson-Lie groups and of similar Poisson manifolds which can be represented as moduli spaces of flat connections on surfaces. The star products depend on a choice of…

In this paper, we construct a smooth vector bundle over the deformation to the normal cone $\text{DNC}(V,M)$ through a rescaling of a vector bundle $E\to V$, which generalizes the construction of the spinor rescaled bundle over the tangent…

We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of…

Let $X$ be a compact connected Riemann surface, and let ${\mathcal Q}(r,d)$ denote the quot scheme parametrizing the torsion quotients of ${\mathcal O}^{\oplus r}_X$ of degree $d$. Given a projective structure $P$ on $X$, we show that the…

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…

In these notes we survey basic concepts of affine geometry and their interaction with Riemannian geometry. We give a characterization of affine manifolds which has as counterpart those pseudo-Riemannian manifolds whose Levi-Civita…

It is shown that for arbitrary connection in the vector bundle compatible with some Hermitian metric, the corresponding Fedosov trace functional commutes with involution generated by this metric. This result is then used to prove that…

Given a Finsler space (M,F), one can define natural average Riemannian metrics on M by averaging on the indicatrix I_x the fundamental tensor g of the Finsler function $F$. In this paper we determine explicitly the Levi-Civita connection…

We study contact 3-manifolds $Y$ with a special global frame inspired by Cartan's structure equations. This frame is dual to a generalized Finsler structure defined by Bryant. We present some examples and rigidity results on the class of…

I have chosen, in this presentation of Deformation Quantization, to focus on 3 points: the uniqueness --up to equivalence-- of a universal star product (universal in the sense of Kontsevich) on the dual of a Lie algebra, the cohomology…

In the present paper we prove a statement closely related to the cyclic formality conjecture. In particular, we prove that for a divergence-free Poisson bivector field on R^d, the Kontsevich star-product with the harmonic angle function is…

We explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentzian $n$-manifold $(M, g)$, equipped with a prescribed optical geometry of K\"ahler-Sasaki type. The formulas found in…