相关论文: Geometric Quantization on Orbifolds

In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the previous cotangent…

Kostant gave a model for the real geometric quantization associated to polarizations via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by…

This is a survey on our recent works which reveal new relationships among deformation quantization, geometric quantization, Berezin-Toeplitz quantization and BV quantization on K\"ahler manifolds.

This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain…

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to…

In this preprint the notion of deformation quantization of endomorphism bundles over symplectic manifolds is defined and developed, including index theory.

We extend Fedosov deformation quantization to general contact manifolds. Unlike the case of symplectic manifolds, not every classical observable on a contact manifold is generally quantized. On examination of possible obstructions to…

We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…

We define prequantization for Dirac manifolds to generalize known procedures for Poisson and (pre) symplectic manifolds by using characteristic distributions obtained from 2-cocycles associated to Dirac structures. Given a Dirac manifold…

In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

The so-called quantization problem in geometric quantization is asking whether the space of wave functions is independent of the choice of polarization. In this paper, we apply SYZ transforms to solve the quantization problem in two cases:…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

We give a classification of polarized deformation quantizations on a symplectic manifold with a (complex) polarization. Also, we establish a formula which relates the characteristic class of a polarized deformation quantization to its…

In this survey article, we discuss some recent progress on geometric analysis on manifold with ends. In the final section, we construct manifolds with ends with oscillating volume functions which may turn out to have a different heat kernel…

We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…

The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results…

In this paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is K\"ahler equipped with transversal complex polarizations $T^{1, 0}X,…

In this paper we find connection between the Hofer's metric of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold, with an integral symplectic form, and the geometry, defined in a paper by Eliashberg and Polterovich,…