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Noncommutative geometry
Non-commutative differential geometry
© Publications mathématiques de l’I.H.É.S., 1985, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
Non-Commutative Geometry
For purely mathematical reasons it is necessary to consider spaces which cannot be represented as point set sand where the coordinates describing the space do not commute.In other words,spaces whichExpand
Gravity coupled with matter and the foundation of non-commutative geometry
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds. Its unitary representations correspondExpand
Renormalization in quantum field theory and the Riemann-Hilbert problem
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann--Hilbert problem.Expand
Hopf Algebras, Renormalization and Noncommutative Geometry
Abstract:We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations.
The Spectral Action Principle
Abstract:We propose a new action principle to be associated with a noncommutative space . The universal formula for the spectral action is where is a spinor on the Hilbert space, is a scale and aExpand
Noncommutative Geometry and Matrix Theory: Compactification on Tori
We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classificationExpand
The Longitudinal Index Theorem for Foliations
In this paper , we use the bivariant K theory of Kasparov ([19]) as a basic tool to prove the K-theoretical version of the index theorem for longitudinal elliptic differential operators forExpand
Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem
Abstract:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedureExpand