Related papers: Polynomial automorphisms, quantization and Jacobia…
A quantum integrable model related to $U_q(\hat{sl}(N))$ is considered. A reduced model is introduced which allows interpretation in terms of quantized affine Jacobi variety. Closed commutation relations for observables of reduced model are…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
The purpose of this paper is twofold: On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational…
We present a panoramic view on various attempts to "solve" the problems of quantum measurement and macro-objectivation, i.e. of the transition from a probabilistic quantum mechanic microscopic world to a deterministic classical macroscopic…
The Newton polytope related to a ``minimal" counterexample to the Jacobian conjecture is introduced and described. This description allows to obtain a sharper estimate for the geometric degree of the polynomial mapping given by a Jacobian…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…
We report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and ``saturation'' properties of several generalizations of the…
This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…
We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization…
Let $ K[x, y]$ be the polynomial algebra in two variables over a field $K$ of characteristic $0$. A subalgebra $R$ of $K[x, y]$ is called a retract if there is an idempotent homomorphism (a {\it retraction}, or {\it projection}) $\varphi:…
The purpose of this note is to clarify the logical relationship between joint measurability and contextuality for quantum observables in view of recent developments [1-4].
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
We survey the theory of the compactified Jacobian associated to a singular curve. We focus on describing low genus examples using the Abel map.
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…