相关论文: The obstruction to the existence of a loopless sta…

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…

The noncommutative star product of phase space functions is, by construction, associative for both non-degenerate and degenerate case (involving only second class constraints) as has been shown by Berezin, Batalin and Tyutin. However, for…

It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on the path component in the cohomology class of the symplectic form and the cohomology class of the closed formal 2-form required to define…

We show that Gammelgaard's formula expressing a star product with separation of variables on a pseudo-Kaehler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal Fock space.…

This article is the first in a series of two in which we study the vanishing cycles of curves in toric surfaces. We give a list of possible obstructions to contract vanishing cycles within a given complete linear system. Using tropical…

We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of…

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 show that every nontrivial finite or infinite connected directed graph with loops and at least one vertex without a loop is uniquely representable as a Cartesian or weak Cartesian product of prime graphs. For finite graphs the…

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…

Comparing the star product defined by Takhtajan on the Poisson-Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any ''K-star product'') on the same group, we show, by direct computation, that the Takhtajan star…

In the present paper we construct the star products concerning scalar fields in the covariant case from a new approach. We construct the star products at three levels, which are levels of functions on Rd, fields and functionals…

A graph $G$ with $p$ vertices and $q$ edges has an antimagic labelling if there is a bijection from the graph's edge set to the label set $\left\{1,2, \cdots, q \right\}$ such that $p$ vertices must have distinct vertex sums, where the…

A formulation of anomalies in terms of star products is suggested which promises insight from an alternative and unifying point of view.

M{\o}ller maps are identifications between the observables of a perturbatively interacting physical system and the observables of its underlying free (i.e. non-interacting) system. This work studies and characterizes obstructions to the…

We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity…

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 give a direct elementary proof of the existence of traces for arbitrary star products on a symplectic manifold. We follow the approach we used in \cite{refs:GuttRaw}, solving first the local problem. A normalisation introduced by…

We extend a key result in [Zha26], by establishing the obstruction that the minimal product structure (for minimal submanifolds or stationary currents in spheres) automatically makes all cones over (non-trivial) minimal products fail to be…

It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an…

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their…