Examples of derivation-based differential calculi related to noncommutative gauge theories
Reads0
Chats0
TLDR
Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented in this paper, and some comparisons between them are made.Citations
More filters
Journal ArticleDOI
Noncommutative epsilon-graded connections
TL;DR: In this paper, the notion of epsilon-graded associative algebras is introduced, which takes its root into the notion for commutation factors introduced in the context of Lie algesbras.
Journal ArticleDOI
On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
TL;DR: In this paper, the authors review the three principal interpretations of this harmonic term: the Langmann-Szabo duality, the superalgebraic approach and the noncommutative scalar curvature interpretation.
Journal ArticleDOI
Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
TL;DR: In this paper, a family of algebras whose noncommutativity is of Lie type was equipped with a derivation-based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four dimensional space.
Gauge field theories: various mathematical approaches
TL;DR: In this paper, the authors present relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids.
Journal ArticleDOI
Module parallel transports in fuzzy gauge theory
TL;DR: A notion of parallel transport on finite projective modules over finite matrix algebras is defined and it is proved that this set of observables is separating on the space of gauge equivalence classes of Hermitian connections, which solves the gauge copy problem for fuzzy gauge theories.
References
More filters
Book
A guide to quantum groups
Vyjayanthi Chari,Andrew Pressley +1 more
TL;DR: In this paper, the Kac-Moody algebras and quasitriangular Hopf algesas were used to represent the universal R-matrix and the root of unity case.
Journal ArticleDOI
Renormalization of gauge theories
C. Becchi,A. Rouet,R. Stora +2 more
TL;DR: Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts as mentioned in this paper.
Journal ArticleDOI
Non-commutative differential geometry
Alain Connes,Alain Connes +1 more
TL;DR: In this paper, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of publication mathématique de l'I.H.É.S.
Journal ArticleDOI
The Fuzzy sphere
TL;DR: A model of Euclidean spacetime is presented in which at scales less than a certain length kappa the notion of a point does not exist and the algebra which determines the structure of the model is an algebra of matrices.