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
Daniel Kastler
Publications and source records attributed to Daniel Kastler.
Connes-Moscovici-Kreimer Hopf Algebras
These notes hopefully provide an aid to the comprehension of the Connes-Moscovici and Connes-Kreimer works, by isolating common mathematical features of the Connes-Moscovici, rooted trees, and Feynman-graph Hopf algebras (as a new special branch of the theory of Hopf algebras expected to become important). We discuss in particular the dual Milnor-Moore situation.
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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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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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