Thursday, January 5, 2012

Quick Neutrino Review

Some years ago we were wondering about the relation between neutrino physics and the McKay correspondence, for the exceptional groups $E_6$, $E_7$ and $E_8$. Much has happened since then, in the twistor world, in the Jordan algebra world, and in the cat world. It is clear that exceptional structures play an important role in gravity.


  1. Kea,

    The thought crossed my mind recently that when it comes to something physical like particles, if not gravity, that these may be the only groups that make a difference. In the Galois conception that irreducible as representations is assumed a particle. How can anyone fail to see the significance of such concepts- especially when, as accurate as the standard theory is it has a long way to go to meet more foundational ideas of super-symmetry as the areas you mention here and results in an equally accurate yet seemingly simpler theory. Are there not 26 such groups? Their subgroups may apply too, then we can see what is useful beyond these- but of course I speak more from the finite group view.

    The PeSla

  2. The PeSla, yes, in the categorical framework we are indeed talking about the classification of finite and Lie groups, and $E_6$, $E_7$ and $E_8$ are known to be special for many reasons, such as their appearance in the magic square for the triplet $C$, $H$, $O$.

    How can anyone fail to understand the importance of the representation-arithmetic correspondence? Simple. They either don't know enough mathematics or they don't know enough physics, or, in most cases, both. To good mathematicians, this is the subject of the Langlands correspondence, but these guys are stuck on the physics of the old standard model, and they tend to believe what stringers like Witten tell them, because, well, you can see all the mathematical connections. Anyway, things are very clearly headed in the right direction now, and I would never have said that until about 1 year ago.


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