Related papers: A Noncommutative Gauss map
We investigate the theory of the bosonic-fermionic noncommutativity, $[x^{\mu},\theta^{\alpha}] = i \lambda^{\mu \alpha}$, and the Wess-Zumino model deformed by the noncommutativity. Such noncommutativity links well-known space-time…
Noncommuting spatial coordinates are studied in the context of a charged particle moving in a strong non-uniform magnetic field. We derive a relation involving the commutators of the coordinates, which generalizes the one realized in a…
We describe basic concepts of noncommutative geometry and a general construction extending the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and Noncommutative algebras. Basic tools…
In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of…
Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the…
We prove the $\Gamma$-convergence of the renormalised fractional Gaussian $s$-perimeter to the Gaussian perimeter as $s\to 1^-$. Our definition of fractional perimeter comes from that of the fractional powers of Ornstein-Uhlenbeck operator…
We study the fixed point for a non-linear transformation in the set of Hausdorff moment sequences, defined by the formula: $T((a_n))_n=1/(a_0+... +a_n)$. We determine the corresponding measure $\mu$, which has an increasing and convex…
We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar $\phi^4$ model with an additional oscillator potential. This model is known to…
In this note the noncommutative geometry is interpreted as a functor, whose range is a family of the operator algebras. Some examples are given and a program is sketched.
This paper shows how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. Discrete calculus is seen to fit into this pattern by reformulating…
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…
We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an…
Our experience shows that dealing with noncommutative objects one should not imitate the classical commutative mathematics, but follow "the way it is" starting with basics. In this paper we consider mainly two such problems: noncommutative…
In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…
By abstracting a connection between gauge symmetry and gauge identity on a noncommutative space, we analyse star (deformed) gauge transformations with usual Leibnitz rule as well as undeformed gauge transformations with a twisted Leibnitz…
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued…
In this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced version, the Gauss map, respectively.…
We prove that certain non-local functionals defined on measurable sets Gamma-converge to the perimeter in the sense of De Giorgi.
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the…