相关论文: Bohr-Sommerfeld Star Products

In this paper we prove the unobstructedness of the deformation of integral coisotropic submanifolds in symplectic manifolds, which can be viewed as a natural generalization of results of Weinstein for Lagrangian submanifolds.

We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

Let $(X,\omega)$ be a symplectic orbifold which is locally like the quotient of a $\mathbb{Z}_2$ action on $\reals^n$. Let $A^{((\hbar))}_X$ be a deformation quantization of $X$ constructed via the standard Fedosov method with…

In this article, we establish the Bohr inequalities for the sense-preserving $K$-quasiconformal harmonic mappings defined in the unit disk $\mathbb{D}$ involving classes of Ma-Minda starlike and convex univalent functions, usually denoted…

This work is the final version of my master thesis. Many, but not all of its key results are already available as a preprint with Chiara Esposito and Stefan Waldmann on arxiv.org under the title "Convergence of the Gutt Star Product", which…

Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to…

The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question,…

In certain neighborhood $U$ of an arbitrary point of a symplectic manifold $M$ we construct a Fedosov-type star-product $\ast_L$ such that for an arbitrary leaf $\wp$ of a given polarization $\mathcal{D}\subset TM$ the algebra $C^\infty…

The purpose of this short note is to establish an explicit equivalence between the two star products $\star$ and $\star_{\log}$ on the symmetric algebra $\mathrm S(\mathfrak g)$ of a finite-dimensional Lie algebra $\mathfrak g$ over a field…

Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the following model…

In the definition of irreducible holomorphic symplectic manifolds the condition of being simply connected can be replaced by vanishing irregularity. We discuss finite quotients X of complex tori where the space of reflexive 2-forms is…

In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are restrictions of deformations on the dual of the Lie algebra. We…

In this remark we discuss a relationship between (co)homology classes of a symplectic manifold realized by symplectic and lagrangian objects. We establish some transversality condition for the classes, realized by symplectic divisors and…

Let \ $\lambda \in \mathbb{Q}^{*+}$ \ and consider a multivalued formal function of the type $$ \phi(s) : = \sum_{j=0}^k \ c_j(s).s^{\lambda + m_j}.(Log\, s)^j $$ where \ $c_j \in \C[[s]], m_j \in \mathbb{N}$ \ for \ $j \in [0,k-1]$. The…

We study the notion of orderability of isotopy classes of Legendrian submanifolds and their universal covers, with some weaker results concerning spaces of contactomorphisms. Our main result is that orderability is equivalent to the…

Let $(X,\omega)$ be a compact symplectic manifold, $L$ be a Lagrangian submanifold and $V$ be a codimension 2 symplectic submanifold of $X$, we consider the pseudoholomorphic maps from a Riemann surface with boundary…

Recently Y{\"u}ksel et. al. \cite{SY} shows that there doesn't exist any proper semi-slant warped product submanifolds in a Lorentzian paracosymplectic manifold. In the present article, we first define and give preparatory lemmas for a new…

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the…

We consider closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordstr\"{o}m manifolds. By using a new integral formula or Brendle's Heintze-Karcher…

In this paper we construct star products on Marsden-Weinstein reduced spaces in case both the original phase space and the reduced phase space are (symplectomorphic to) cotangent bundles. Under the assumption that the original cotangent…