相关论文: Quantum moment map and obstructions to the existen…

We study obstructions to the existence of closed Fedosov's star products on a given K\"ahler manifold. In our previous paper, we proved that the Levi-Civita connection of a K\"ahler manifold will produce a closed (in the sense of…

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…

In these notes we consider the usual Fedosov star product on a symplectic manifold $(M,\omega)$ emanating from the fibrewise Weyl product $\circ$, a symplectic torsion free connection $\nabla$ on M, a formal series $\Omega \in \nu…

We deform the moment map picture on the space of symplectic connections on a symplectic manifold. To do that, we study a vector bundle of Fedosov star product algebras on the space of symplectic connections. We describe a natural formal…

We study the Cahen-Gutt moment map on the space of symplectic connections of a symplectic manifold. On a K\"ahler manifold, we define a Calabi-type functional $\mathscr{F}$ on the space of K\"ahler metrics in a given K\"ahler class. We…

The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on…

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…

In this note we classify invariant star products with quantum momentum maps on symplectic manifolds by means of an equivariant characteristic class taking values in the equivariant cohomology. We establish a bijection between the…

We associate quantum states with subsets of a product of two compact connected K\"ahler manifolds $M_1$ and $M_2$. To associate the quantum state with the subset, we use the map that restricts holomorphic sections of the quantum line bundle…

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold $\mathcal M$ is presented as a…

The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star…

We show that if a compact Kaehler manifold $M$ of non-negative Ricci curvature admits closed Fedosov star product then the reduced Lie algebra of holomorphic vector fields on $M$ is reductive. This comes in pair with the obstruction…

In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of Wick type on every K\"ahler manifold by a…

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 various aspects of Fedosov star-products on symplectic manifolds. By introducing the notion of "quantum exponential maps", we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is…

We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…

Given a Lie group acting on a manifold $M$ preserving a closed $n+1$-form $\omega$, the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6], in terms of $L_{\infty}$-algebra morphisms. In this…

We extend our investigations on $\mathfrak g$-invariant Fedosov star products and quantum momentum mappings \cite{MN03a} to star products of Wick type on pseudo-K\"ahler manifolds. Star products of Wick type can be completely characterized…

Take a closed monotone symplectic manifold containing a smooth anticanonical divisor. The quantum connection on its cohomology has singularities at zero and infinity (in the quantum parameter). At zero it has a regular singular point, by…

In part I, using the theory of $\infty$-categories, we constructed a natural ``continuous action'' of $\operatorname {Ham} (M, \omega) $ on the Fukaya category of a closed monotone symplectic manifold. Here we show that this action is…