Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Share This Author

Non-commutative differential geometry

- A. Connes
- Mathematics
- 1 December 1985

© 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

- A. Connes
- Physics
- 1988

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 which… Expand

Gravity coupled with matter and the foundation of non-commutative geometry

- A. Connes
- Mathematics, Physics
- 8 March 1996

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 correspond… Expand

Renormalization in quantum field theory and the Riemann-Hilbert problem

- A. Connes, D. Kreimer
- Physics, Mathematics
- 17 September 1999

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

- A. Connes, D. Kreimer
- Mathematics, Physics
- 7 August 1998

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

- A. Chamseddine, A. Connes
- Physics
- 3 June 1996

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 a… Expand

Noncommutative Geometry and Matrix Theory: Compactification on Tori

- A. Connes, M. Douglas, A. Schwarz
- Physics
- 20 November 1997

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 classification… Expand

The Longitudinal Index Theorem for Foliations

- A. Connes, G. Skandalis
- Mathematics
- 31 December 1984

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 for… Expand

Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

- A. Connes, D. Kreimer
- Physics, Mathematics
- 13 December 1999

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 procedure… Expand

...

1

2

3

4

5

...