Related papers: Quantization in fibering polarizations, Mabuchi ra…

Let $(M, \omega)$ be a K\"ahler manifold and let $(L, \nabla)$ be a prequantum line bundle over $M$. Let $X \subset M$ be a Bohr-Sommerfeld Lagrangian submanifold of $(L, \nabla)$. In this paper, we study an asymptotic behaviour of…

We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…

We relate Berezin-Toeplitz quantization of higher rank vector bundles to quantum-classical hybrid systems and quantization in stages of symplectic fibrations. We apply this picture to the analysis and geometry of vector bundles, including…

We addressed quantization phenomena in transport and vortex/precession-motion of low-dimensional systems, stationary quantization of confined motion in phase space due to oscillatory dynamics or compacti fication of space and time for…

A normal form transformation is carried out on the operators of a complete set of commuting observables in a multidimensional, integrable quantum system, mapping them by unitary conjugation into functions of the harmonic oscillators in the…

We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-K\"ahler polarizations which occur generically on…

We prove the convergence of geodesic distance during the quantization of the space of K\"ahler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The…

We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the…

We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…

We derive a $K$-theoretic analogue of the Vafa--Intriligator formula, computing the (virtual) Euler characteristics of vector bundles over the Quot scheme that compactifies the space of degree $d$ morphisms from a fixed projective curve to…

We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…

The first part of this thesis studies the notion of a "quantum representation", introduced by J.-M. Souriau in order to provide a polarization-free characterization of the Lie group representations attached to coadjoint orbits. When the…

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between…

We determine the wave functions for arbitrarily polarized quantum Hall states by employing the doublet model which has been proposed recently to describe arbitrarily polarized quantum Hall states. Our findings recover the well known fully…

We consider the relative canonical line bundle $K_{\mathcal{X}/\mathcal{T}}$ and a relatively ample line bundle $(L, e^{-\phi})$ over the total space $ \mathcal{X}\to \mathcal{T}$ of fibration over the Teichm\"uller space by Riemann…

We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kahler manifolds and show the necessity of the Kahler condition. For torus…

In this article we describe the $\tG\times \tG$-equivariant $K$-ring of $X$, where $\tG$ is a {\it factorial} cover of a connected complex reductive algebraic group $G$, and $X$ is a regular compactification of $G$. Furthermore, using the…

I construct lowest-energy representations of non-centrally extended algebras of Noether symmetries, including diffeomorphisms and reparametrizations of the observer's trajectory. This may be viewed as a new scheme for quantization. First…

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…