Remarks on Alain Connes' approach to the standard model
Our 1992 remarks about Alain Connes' interpretation of the standard model within his theory of non-commutative riemannian spin manifolds.
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arXiv subjects
Thomas Schucker
Publications and source records attributed to Thomas Schucker.
Spectral action beyond the standard model
We rehabilitate the M_1(C)+ M_2(C)+ M_3(C) model of electro-magnetic, weak and strong forces as an almost commutative geometry in the setting of the spectral action.
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Non-commutative Geometry Beyond the Standard Model
A natural extension of the standard model within non-commutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
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Spin group and almost commutative geometry
For Connes' spectral triples, the group of automorphisms lifted to the Hilbert space is defined and used to fluctuate the metric. A few commutative examples are presented including Chamseddine and Connes' spectral unification of gravity and electromagnetism. One almost commutative example is treated: the full standard model. Here the lifted automorphisms explain O'Raifeartaigh's reduction $SU(2)\times U(3)/\zz_2.$
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Standard model and unimodularity condition
The unimodularity condition in Connes' formulation of the standard model is rewritten in terms of group representations.
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Noncommutative Yang-Mills and Noncommutative Relativity: A Bridge Over Trouble Water
Connes' view at Yang-Mills theories is reviewed with special emphasis on the gauge invariant scalar product. This landscape is shown to contain Chamseddine and Connes' noncommutative extension of general relativity restricted to flat space-time, if the top mass is between 172 and 204 GeV. Then the Higgs mass is between 188 and 201 GeV.
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On Connes' new principle of general relativity. Can spinors hear the forces of spacetime?
Connes has extended Einstein's principle of general relativity to noncommutative geometry. The new principle implies that the Dirac operator is covariant with respect to Lorentz and internal gauge transformations and the Dirac operator must include Yukawa couplings. It further implies that the action for the metric, the gauge potentials and the Higgs scalar is coded in the spectrum of the covariant Dirac operator. This ``universal'' action has been computed by Chamseddine & Connes, it is the coupled Einstein-Hilbert and Yang-Mills-Higgs action. This result is rederived and we discuss the physical consequences.
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On the universal Chamseddine-Connes action 1. Details of the action computation
We give the details of the computation of the Chamseddine-Connes action by combination of a Lichnerowicz formula with the heat kernel expension.
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The Noncommutative Constraints on the Standard Model à la Connes
Noncommutative geometry applied to the standard model of electroweak and strong interactions was shown to produce fuzzy relations among masses and gauge couplings. We refine these relations and show then that they are exhaustive.
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Riemannian and Non-commutative Geometry in Physics
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
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Fuzzy Mass Relations in the Standard Model
Recently Connes has proposed a new geometric version of the standard model including a non-commutative charge conjugation. We present a systematic analysis of the relations among masses and coupling constants in this approach. In particular, for a given top mass, the Higgs mass is constrained to lie in an interval. Therefore this constraint is locally stable under renormalization flow.
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A DETAILED ACCOUNT OF ALAIN CONNES' VERSION OF THE STANDARD MODEL IV
We give a detailed account of the computation of the Yang-Mills action for the Connes-Lott model with general coupling constant in the commutant of the $K$-cycle. This leads to tree-approximation results amazingly compatible with experiment, yielding a first indication on the Higgs mass.
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The Standard Model a la Connes-Lott
The relations among coupling constants and masses in the standard model à la Connes-Lott with general scalar product are computed in detail. We find a relation between the top and the Higgs masses. For $m_t=174\pm22\ GeV$ it yields $m_H=277\pm40\ GeV$. The Connes-Lott theory privileges the masses $m_t=160.4\ GeV$ and $m_H=251.8\ GeV$.
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A Left-Right Symmetric Model a la Connes-Lott
We present a left-right symmetric model with gauge group $U(@)_L\times U(@)_R$ in the Connes-Lott non-commutative frame work. Its gauge symmetry is broken spontaneously, parity remains unbroken.
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