Related papers: Toeplitz Quantization and Asymptotic Expansions: G…

We present a systematic quantization scheme for bounded symplectic domains of the form $D \times G \subset T^\ast G$, where $D \subset \mathfrak{g}^\ast$ is a bounded region defined by algebraic inequalities and $G$ is a compact Lie group…

In this paper we use orthonormal basis for the Hardy space $H^{2}(\mathbb{T})$, formed by rational functions, to characterize complex symmetric Toeplitz operators on $H^{2}(\mathbb{T})$. As a result, we get examples of these operators whose…

The present work represents a step to deal with stellar structure using a pure geometric approach. A geometric field theory is used to construct a model for a spherically symmetric configuration. The model obtained can be considered as a…

We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…

The purpose of this short note is to establish an explicit equivalence between 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…

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 paper, we construct a family of Berezin-Toeplitz type quantizations of a compact symplectic manifold. For this, we choose a Riemannian metric on the manifold such that the associated Bochner Laplacian has the same local model at…

Let $(G,\kappa)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain…

We introduce a method of geometric quantization for compact $b$-symplectic manifolds in terms of the index of an Atiyah-Patodi-Singer (APS) boundary value problem. We show further that b-symplectic manifolds have canonical Spin-c structures…

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators,…

The main results of this paper are an asymptotic expansion in powers of $\hbar$ for the spectral measure $\mu_\hbar$ of a semi-classical Toeplitz operator, $Q_\hbar$, and an equivariant version of this result when $Q_\hbar$ admits an…

We describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It brings us to a…

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang…

We provide a new general scheme for the geometric quantisation of $\operatorname{Sp}(1)$-symmetric hyper-K\"ahler manifolds, considering Hilbert spaces of holomorphic sections with respect to the complex structures in the hyper-K\"ahler…

In this article, we determine the spectrum of real-analytic, non self-adjoint Toeplitz operators on compact K{\"a}hler manifolds and on the complex plane, on neighbourhoods of critical values of the symbol. We consider specifically critical…

For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I [Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain dynamical aspects of the model as controlled by the external, rotation-symmetric…

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…

The asymptotic expansion of the Kummer function ${}_1F_1(a; b; z)$ is examined as $z\to+\infty$ on the Stokes line $\arg\,z=0$. The correct form of the subdominant algebraic contribution is obtained for non-integer $a$. Numerical results…

Geometric Quantization is a term used to describe a wide collection of techniques dating back to the 1960s in the work of Kirillov, Kostant, and Souriau, which take symplectic manifolds and produce complex vector spaces. The name comes from…

Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies…