Results 21 to 30 of about 16,964 (172)

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

Connes' noncommutative differential geometry and the standard model

Journal of Geometry and Physics, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Várilly Boyle, Joseph C., Gracia Bondía, José M.   +1 more
openaire   +4 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

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 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

BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry [PDF]

, 1999
Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space.
Connes Alain, Kugo T., Lee C. Y., Martı́n C. P., Morita K., Morita K., Okumura Y., Okumura Y., Okumura Y., Okumura Y., Okumura Y., Okumura Y., Okumura Y., Yoshitaka Okumura   +13 more
core   +3 more sources

Quantization of infinitesimal braidings and pre‐Cartier quasi‐bialgebras

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract In this paper, we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the nonsymmetric case. The algebraic counterpart of these categories is the notion of a pre‐Cartier quasi‐bialgebra, which extends the well‐known notion of quasi‐triangular quasi‐bialgebra given by Drinfeld.
Chiara Esposito, Andrea Rivezzi, Jonas Schnitzer, Thomas Weber   +3 more
wiley   +1 more source

Plank theorems and their applications: A survey

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley   +1 more source