Urs tutorial on Connes spectral geometry

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Discussion Overview

The discussion revolves around Alain Connes' work on spectral geometry and its implications for understanding the Standard Model in physics. Participants explore the nuances of noncommutative geometry, the role of dimensionless constants, and the potential for deriving properties of the Standard Model from spectral triples. The conversation includes references to related theories and critiques of string theory, as well as informal exchanges about terminology and concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants express skepticism about the term "noncommutative geometry," suggesting it may be more accurately described as "spectral geometry," as proposed by Urs.
  • John Baez questions Connes' ability to derive the correct dimensionless constants in the Standard Model Lagrangian, noting that if he had succeeded, it would have significant implications.
  • Urs argues that the goal of Connes' work is not necessarily to predict the Standard Model's properties but to identify the spectral triple that describes it, emphasizing the elegance of such a description.
  • Some participants note that while Connes' approach may appear to be repackaging existing ideas, it reveals intriguing mathematical relationships worth studying.
  • There is a discussion about the implications of curvature in the context of string theory and the Landscape, with varying opinions on its predictability and scientific validity.
  • Participants engage in a light-hearted exchange about the term "Gelfandry," with attempts to define it and its implications in the context of algebraic descriptions of geometry.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the effectiveness of Connes' approach or the implications of his work. There are multiple competing views regarding the significance of dimensionless constants and the validity of string theory, indicating an unresolved discussion.

Contextual Notes

Some participants express uncertainty about specific terms and concepts, such as "Gelfandry," and the mathematical underpinnings of Connes' work. The discussion reflects a range of interpretations and assumptions that are not fully clarified.

  • #31
Now I imagine that g is something like a simplex, only perhaps with a dimension along the possible worldlines included. Is this the idea?

I am going to listen to Connes as Marcus suggested in an earlier post, as I have now temporary access to a broadband bubble.

R.

Seems I can't understand the talk...maybe accent problem, or microphone, or my inability to recognise the concept vocabulary.

Oh well. Back to reading.

R
 
Last edited:
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  • #32
the idea is , if you drop commutativity of the derivative and similar then you define

the 'derivative' of f respect to 'x' as \frac{df}{dx}= [f, A]

but the question is what is 'A' operator ??

and for the 'integral' how can you define or justify this

\int f |D| = Res_{s=0} Tr( f |D|^{-s} )

and it would be so simple as this ? you would replace the 'normal' derivative and integral by taking a Trace or commutators ??
 

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