Results 21 to 30 of about 16,979 (167)

Deformation quantization and intrinsic noncommutative differential geometry

, 2023
We provide an intrinsic formulation of the noncommutative differential geometry developed earlier by Chaichian, Tureanu, R. B. Zhang and the second author. This yields geometric definitions of covariant derivatives of noncommutative metrics and curvatures, as well as the noncommutative version of the first and the second Bianchi identities.
Gao, Haoyuan, Zhang, Xiao
openaire   +2 more sources

Noncommutative scalar fields: Quantum symmetries and braided BV quantization [PDF]

Kragujevac Journal of Science
It is strongly believed that the fully consistent quantum gravity theory should lead to a quantum spacetime. The continuous description of spacetime in terms of differential manifolds is no longer adequate at the quantum gravity energies.
Bežanić Milorad, Bogdanović Đorđe, Dimitrijević-Ćirić Marija   +2 more
doaj   +1 more source

A new algebraic structure in the standard model of particle physics

Journal of High Energy Physics, 2018
We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to
Latham Boyle, Shane Farnsworth
doaj   +1 more source

Examples of derivation-based differential calculi related to noncommutative gauge theories

, 2008
Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in
Chari V., Connes A., Connes A., Dubois-Violette M., Dubois-Violette M., Dubois-Violette M., Gracia-Bondia J. M., Kerner R., Kerner R., Masson T., T. MASSON, Wallet J.-C.   +11 more
core   +2 more sources

Noncommutative Geometry and Gravity

, 2005
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product.
Aschieri, Paolo, Dimitrijevic, Marija, Meyer, Frank, Wess, Julius   +3 more
core   +2 more sources

Noncommutative differential geometry on infinitesimal spaces

Annales mathématiques du Québec
In this paper, we use the language of noncommutative differential geometry to formalise discrete differential calculus. We begin with a brief review of inverse limit of posets as an approximation of topological spaces. We then show how to associate a $C^*$-algebra over a poset, giving it a piecewise-linear structure.
Tageddine, Damien, Nave, Jean-Christophe
openaire   +2 more sources

Examples of noncommutative manifolds: complex tori and spherical manifolds

, 2007
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the differential geometry
Plazas, Jorge
core   +2 more sources

The Serre spectral sequence of a noncommutative fibration for de Rham cohomology

, 2005
For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces.
A. Connes, A. V. Rojter, D. E. Evans, E. J. Beggs, Edwin J. Beggs, H.-J. Schneider, I. Heckenberger, J. Bénabou, J. Madore, J. McCleary, J. W. Milnor, M. E. Sweedler, M. Kontsevich, P. Podleś, R. Street, S. Caenepeel, S. L. Woronowicz, S. L. Woronowicz, S. Lack, S. Majid, T. Brzeziński, T. Brzeziński, T. Brzeziński, Tamasz Brzeziński   +23 more
core   +1 more source

Quantum Frustration as a Protection Mechanism in Non‐Topological Majorana Qubits

Annalen der Physik, Volume 538, Issue 4, April 2026.
Quantum frustration is proposed as a robust protection mechanism for non‐topological ‐junction qubit. By leveraging distinct spatial profiles, co‐located Majorana modes couple to independent environments, creating incompatible pointer bases that suppress decoherence.
E. Novais
wiley   +1 more source

Closed Form Relations and Higher‐Order Approximations of First and Second Derivatives of the Tangent Operator on SE(3)

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