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Why the Standard Model · Around

2007

Why the Standard Model

Chamseddine, Ali H., Connes, Alain

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The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding.

We propose a purely gravitational explanation: space-time has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F.
The raison d'etre for F is to correct the K-theoretic dimension from four to ten (modulo eight).
We classify the irreducible finite noncommutative geometries of K-theoretic dimension six and show that the dimension (per generation) is a square of an integer k.

Built on

M.F. Atiyah. Geometry of Yang-Mills fields. Accad. Naz. dei Lincei, Scuola Norm. Sup., Pisa,
1979
Earlier work this paper cites.
A. Chamseddine, G. Felder and J. Fröhlich, Unified Gauge theories in Noncommutative Geometry
1992
Earlier work this paper cites.
A. Connes, Noncommutative geometry
1994
Earlier work this paper cites.
A. Connes, Non commutative geometry and reality
1995
Earlier work this paper cites.

Similar

A. Connes, Gravity coupled with matter and the foundation of noncommutative geometry
1995
Cited alongside, same era.
A. Chamseddine, A. Connes, Universal Formula for Noncommutative Geometry Actions: Unification of Gravity and the Standard Model
1996
Cited alongside, same era.
J. Dixmier, Les C*-algèbres et leurs representations
1996
Cited alongside, same era.
A. Chamseddine, A. Connes, The Spectral Action Principle
1997
Cited alongside, same era.
A. Chamseddine, A. Connes, M. Marcolli, Gravity and the standard model with neutrino mixing
Cited in the paper.
A. Connes, A. Chamseddine, Inner fluctuations of the spectral action
Cited in the paper.
A. Connes, M. Marcolli Noncommutative geometry from quantum fields to motives
Cited in the paper.

Then

M. Mehta, Random matrices
2004
Later among the works it cites.
A. Chamseddine, A. Connes, Scale Invariance in the Spectral Action
2006
Later among the works it cites.
A. Connes, Noncommutative Geometry and the standard model with neutrino mixing
2006
Later among the works it cites.
John Barrett, ”The Lorentzian Version of the Noncommutative Geometry Model of Particle Physics”, J. Math. Phys
2007
Closest in time.

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