Results 41 to 50 of about 32,076 (212)
Noncommutative Generalization of Wilson Lines
, 2014 A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths.
Ivankov, Petr
core +1 more source
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 4, April 2026.ABSTRACT The Lie group SE3$SE\left(3\right)$ of isometric orientation‐preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the exponential map, its right‐trivialized differential (often referred to as the tangent operator ...
Andreas Müller
wiley +1 more source
Derivations of the Moyal Algebra and Noncommutative Gauge Theories
Symmetry, Integrability and Geometry: Methods and Applications, 2009 The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections ...
Jean-Christophe Wallet
doaj +1 more source
A geometric picture of quantum mechanics with noncommutative values for observables
Results in Physics, 2020 We present here what we consider a new picture of quantum mechanics with the position and momentum observables as coordinates of the usual quantum phase space of a single particle, which also serves as the model of the physical space.
Otto C.W. Kong
doaj +1 more source
Noncommutative Geometry and MOND
Journal of High Energy Physics, Gravitation and Cosmology, 2022 Modified Newtonian dynamics (MOND) is a hypothesized modification of Newton's law of universal gravitation to account for the flat rotation curves in the outer regions of galaxies, thereby eliminating the need for dark matter. Although a highly successful model, it is not a self-contained physical theory since it is based entirely on observations.
openaire +2 more sources
Noncommutative polygonal cluster algebras
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg +3 more
wiley +1 more source
Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley +1 more source
Dirac Operators on Noncommutative Curved Spacetimes
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy ...
Alexander Schenkel +1 more
doaj +1 more source
Vacuum energy from noncommutative models
Physics Letters B, 2018 The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory.
S. Mignemi, A. Samsarov
doaj +1 more source
Noncommutative Geometry: Calculation of the Standard Model Lagrangian [PDF]
, 2001 The calculation of the standard model Lagrangian of classical field theory within the framework of noncommutative geometry is sketched using a variant with 18 parameters.
Elsner, Karen
core +3 more sources