Related papers: On a Full Quantization of the Torus
After global completion of higher gauge fields (as appearing in higher-dimensional supergravity) by proper flux quantization in extraordinary nonabelian cohomology, the (non-perturbative, renormalized) topological quantum observables and…
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 paper shows that quantization induces a Lawvere-Tierney topology on (hence, a sheaf topos in) the quantum topos. We show that a quantization map from classical observables to self-adjoint operators on a Hilbert space naturally induces…
Let $\TT$ be a torus. We prove that all subsets of $\TT$ with finitely many boundary components (none of them being points) embed properly into $\CC^2$.
We show that a natural complexification and a mild generalization of the idea of completeness guarantee geodesic completeness of Clifton-Pohl torus; we explicitely compute all of its geodesics.
We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the…
We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding…
The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one…
We consider the nondistortion quantum interrogation (NQI) of an atom prepared in a quantum superposition. By manipulating the polarization of the probe photon and making connections to interaction free measurements of opaque objects, we…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
Considering quantales as generalised noncommutative spaces, we address as an example a quantale Pen based on the Penrose tilings of the plane. We study in general the representations of involutive quantales on those of binary relations, and…
The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the quantum grassmannian. More precisely, under the assumption that the deformation parameter $q$ is transcendental, we show that…
In this paper we study the effect of a torus topology on Loop Quantum Cosmology. We first derive the Teichmueller space parametrizing all possible tori using Thurston's theorem and construct a Hamiltonian describing the dynamics of these…
Consider a locally compact group $G=Q\ltimes V$ such that $V$ is abelian and the action of $Q$ on the dual abelian group $\hat V$ has a free orbit of full measure. We show that such a group $G$ can be quantized in three equivalent ways: (1)…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We prove the 2-torus $\mathbb T$, an abelian linear algebraic group, is a fine moduli space of labeled, oriented, possibly-degenerate inscribable similarity classes of triangles, where a triangle is {\it inscribable} if it can be inscribed…
We start by describing the relationship between the classical prequantization condition and the integrability of a certain Lie algebroid associated to the problem and use this to give a global construction of the prequantizing bundle in…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
It is shown that any finite complete covering of a non-commutative algebra in the sense of Calow and Matthes (J. Geom. Phys. 32 (2000), 114--165) gives rise to a Galois coring.
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…