Sunday, July 10, 2011

Theory Update 92

Recall that the $2 \times 2$ Fourier operator $F_2$ is just the Hadamard gate. Observe that under the Jordan product, this is an inverse to our operator $Q$. Since we also allow complex matrix algebras, the Fourier operator is there to turn diagonals into circulants, as it does for the $3 \times 3$ ternary Koide mass matrices.

A child could understand quantum gravity. Perhaps the stringers should be sent back to kindergarten.


  1. Oh look, more fairy field exclusions from the LHC. Well, what physicist ever thought that mass was about fairy fields, anyway?

  2. Actually the data peak "Observed" around 200 GeV is above both the green and yellow Brazil bands which indicates that the new LHC data is not excluding Higgs there,
    is effectively seeing more-than-2-sigma evidence for a Higgs there. Lubos calls it (on Philip Gibbs's blog) "... a near 3 sigma excess ...".


  3. Tony, if fairy fields must exist, then best it be a triplet, as you advocate. However, you cannot be serious about taking 2 sigma seriously.

  4. Here's a wacky idea. It's proposed that motivically obtained amplitudes should be the simplest, and that they will be realized, or at least approximated, by twistor variables. It's also proposed that exceptional measurement algebras (quaternionic or octonionic) play a fundamental role.

    I happened to run across "Quasi-Optimal Arithmetic for Quaternion Polynomials". "Fast algorithms for arithmetic on real or complex polynomials are well-known... [b]ased on Fast Fourier Transform..." The author would like to find something analogous for quaternion polynomials, but can't even define the latter to his satisfaction. Nonetheless, I wonder if there might be ideas here for the concrete formulae playing a role in a motivic physics employing hypercomplex numbers.

    By the way, there are theoretical bounds on how efficient such formulae can be, in which polylogarithms appear. It would be really amazing if that was yet another connection to motives - perhaps the bounds can be conceived geometrically, as hypervolumes, and the methods of calculation which saturate the bounds correspond to optimal motivic methods of amplitude calculation.

  5. Mitchell, nobody is stopping you doing your own research.


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