Related papers: Hitchin systems and their quantization
What makes quantum information science a science? These notes explore the idea that quantum information science may offer a powerful approach to the study of complex quantum systems. We discuss how to quantify complexity in quantum systems,…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
It is shown that quantized dynamical system with second class constraints has infinite dimensional Hilbert space.
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…
In this note we prove a weighted version of the Khintchine inequalities.
The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
We present a gauge-theoretic interpretation of the "analytic" version of the geometric Langlands program, in which Hitchin Hamiltonians and Hecke operators are viewed as concrete operators acting on a Hilbert space of quantum states. The…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006. Typos corrected, some refernces added.
The talk consisted mainly in commenting in a linear way the seminal paper in 1964 by Michel Henon and graduate student Carl Heiles at Princeton University: "The applicability of the third integral of motion: Some numerical experiments" in…
This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…
This is a set of lecture notes for the first author's lectures on the difference equations in 2019 at the Institute of Advanced Study for Mathematics at Zhejiang University. We focus on explicit computations and examples. The convergence of…
We find a worldsheet realization of generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. The two-dimensional model we construct is a supersymmetric relative of…
We continue in this paper our program of rederiving all quantum mechanical formalism from the classical one. We now turn our attention to the derivation of the second quantized equations, both for integral and half-integral spins. We then…
We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce the natural complexified analogue of the Hitchin connection in K\"{a}hler quantisation, with…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Computability Theory and Descriptive Set Theory, June 16-20, 2025. The problems are organized into sections named after their contributors, in…
These are expanded notes of author's talk at the ECM 2008 attempting to give an elementary introduction into the main ideas of the theory of wheeled props for beginners, and also a survey of its most recent major applications (ranging from…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
I give an overview of some of the most used measures of entanglement. To make the presentation self-contained, a number of concepts from quantum information theory are first explained. Then the structure of bipartite entanglement is studied…