Related papers: Dequantization of real algebraic geometry on logar…
We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf…
One of the difficulties in doing noncommutative projective geometry via explicitly presented graded algebras is that it is usually quite difficult to show flatness, as the Hilbert series is uncomputable in general. If the algebra has a…
We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles. For this purpose, we build both the associated quantum…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
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…
This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on…
The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…
Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been…
In this work we give a deformation theoretical approach to the problem of quantization. First the notion of a deformation of a noncommutative ringed space over a commutative locally ringed space is introduced within a language coming from…
In this paper, deformations of $L_\infty$-algebras are defined in such a way that the bases of deformations are $L_\infty$-algebras, as well. A universal and a semiuniversal deformation is constructed for $L_\infty$-algebras, whose…
A non-singular connected algebraic curve $A$ in a simply connected algebraic surface $X$ can be knotted so that its homology class and the fundamental group of its complement in $X$ is preserved, provided $A$ is sufficiently complex (not…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotopy deformation, geometric constructions in computer aided…
In this paper we study the local behavior of an algebraic curve under a geometric construction which is a variation of the usual offsetting construction, namely the {\it generalized} offsetting process (\cite {SS99}). More precisely, here…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
We study a deformed $su(m|n)$ algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed…
We study deformation quantizations of the structure sheaf O_X of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of O_X…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…