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Connes's noncommutative geometry program includes an approach to the Standard Model that employs a noncommutative extension of Riemannian metric. In recent years I've heard physicists say that this approach does not hold significant interest in the physics community.

Is this, in fact, the case? If so, why?

I do not mean for this question to be argumentative, but instead would like clarification.

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Related: physics.stackexchange.com/q/8999/2451 –  Qmechanic Nov 13 '12 at 15:13
Noncommutative geometry can have applications in M-theory, see here –  Dilaton Nov 13 '12 at 15:53
@Qmechanic: The first question partially answers my question, I think... –  Jon Bannon Nov 13 '12 at 18:46
In light of Qmechanic's link, and the fact that we now know the Higgs mass is a little less than 130, can the NCG picture be successfully modified to fit the actual Higgs mass? –  Jon Bannon Nov 13 '12 at 20:07
If you are wondering about the use of noncommutative geometry in physics in general, I think that the most down-to-Earth use is probably Bellissard's use of NCG to explain the integer quantum hall effect. As far as I know, it is the only model of the integer quantum hall effect that takes into account all physical phenomena that are actually present. The Non-Commutative Geometry of the Quantum Hall Effect –  Jon Paprocki Feb 8 '13 at 1:47
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1 Answer

up vote 5 down vote accepted


arXiv:1208.1030 "Resilience of the Spectral Standard Model"

arXiv:1208.5023 "Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models"

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Thanks, Dev. These papers certainly help. I'll accept the answer in light of the fact that the first paper seems to place NCG back in the game. –  Jon Bannon Feb 10 '13 at 15:05
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