Alain Connes (; born 1 April 1947 ) is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University.

Alain Connes is one of the leading specialists on operator algebras.

* Alain Connes and Matilde Marcolli: Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 978-0821842102

* Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger, Jennifer Gage ( translator ): Triangle of Thought, American Mathematical Society, 2001, ISBN 978-0821826140

* Jean-Pierre Changeux, Alain Connes, M. B. DeBevoise ( translator ): Conversations on Mind, Matter, and Mathematics, Princeton University Press, 1998, ISBN 978-0691004051

* Alain Connes: Noncommutative Geometry, Academic Press, 1994, ISBN 978-0121858605

* Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X.

* nlab about Alain Connes

* An interview with Alain Connes and a discussion about it

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* Alain Connes's Standard Model.

Elite Model Management was founded in Paris, France in 1972 by John Casablancas and Alain Kittler.

* Chamseddine, A., A. Connes, M. Marcolli ( 2007 ) " Gravity and the Standard Model with neutrino mixing ," Adv.

The Colt line now includes a new scattergun, the Standard or Custom Pump Model ( about $90 and $150, respectively ) in 12, 16 and 20.

In the Standard Model of physics, electrons are truly elementary particles with no internal structure.

Dark energy in its simplest formulation takes the form of the cosmological constant term in Einstein's field equations of general relativity, but its composition and mechanism are unknown and, more generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both observationally and theoretically.

Precise modern models of the Big Bang appeal to various exotic physical phenomena that have not been observed in terrestrial laboratory experiments or incorporated into the Standard Model of particle physics.

Within the prevailing Standard Model of particle physics, the number of baryons may change in multiples of three due to the action of sphalerons, although this is rare and has not been observed under experiment.

In the 1950s – 1970s, Caltech was the home of Murray Gell-Mann and Richard Feynman, whose work was central to the establishment of the Standard Model of particle physics.

* Conservation of lepton number ( In the Standard Model )

In the Standard Model, the

The Standard Model of elementary particles, with the fermions in the first three columns and the gauge bosons in the fourth column.

Standard Model of elementary particles

In the Standard Model of particle physics, the elementary particles include the fundamental fermions ( including quarks, leptons, and their antiparticles ), and the fundamental bosons ( including gauge bosons and the Higgs boson ).

According to the Standard Model, all elementary particles are either bosons or fermions ( depending on their spin ).

Such particles lie beyond the Standard Model.

The Standard Model of particle physics contains 12 flavors of elementary fermions, plus their corresponding antiparticles, as well as elementary bosons that mediate the forces and the Higgs boson, which was reported on July 4th, 2012, as having been likely detected by the two main experiments at the LHC ( ATLAS and CMS ).

However, the Standard Model is widely considered to be a provisional theory rather than a truly fundamental one, since it is not known if it is compatible with Einstein's general relativity.

There may be hypothetical elementary particles not described by the Standard Model, such as the graviton, the particle that would carry the gravitational force, and sparticles, supersymmetric partners of the ordinary particles.

The Standard Model recognizes two types of elementary fermions: quarks and leptons.

Gravitons are postulated because of the great success of quantum field theory ( in particular, the Standard Model ) at modeling the behavior of all other known forces of nature as being mediated by elementary particles: electromagnetism by the photon, the strong interaction by the gluons, and the weak interaction by the W and Z bosons.

In contrast, the Standard Model is not background independent, with Minkowski space enjoying a special status as the fixed background space-time.

Attempts to extend the Standard Model or other quantum field theories by adding gravitons run into serious theoretical difficulties at high energies ( processes involving energies close to or above the Planck scale ) because of infinities arising due to quantum effects ( in technical terms, gravitation is nonrenormalizable ).

A Grand Unified Theory, ( GUT ), is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant.

In contrast, the experimentally verified Standard Model of particle physics is based on three independent interactions, symmetries and coupling constants.

, all GUT models which aim to be completely realistic are quite complicated, even compared to the Standard Model, because they need to introduce additional fields and interactions, or even additional dimensions of space.

The fact that the electric charges of electrons and protons seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics.