An Exceptionally Technical Discussion of AESToE

garrett

http://deferentialgeometry.org/epe/

MTd2

Garrett, would mind putting a different representation instead of colors. I am color blind, and sometimes I can't tell apart heads and tails.

Also, what is your "my standard model"?

arivero

related some grouping of 6 and the projections having sort of hexagonal symmetry in your gadget: I was reading now a series of lectures on Duality Symmetries, by A. Sen in Les Houches in the 2001 session, and for the 4 dimensional duality of SO(32) heterotic, compacted with T^6, some groups of 6 appear:
- a symmetric 6x6 matrix, giving 21 scalars
- an antisymmetric 6x6, giving 15 scalars
- a 6x16 object giving 96 scalars, related to "the gauge fields in the Cartan subalgebra of the gauge group".
Sen refers to his fundational paper hep-th/9402002 for more info. It is a dense paper, but one can search for the number 16 :-)

I can not bet for an interpretation of the 21 and 15. An interesting observation is that if one reduces the standard model to SU(3)xU(1) then both the neutrinos and the top are lost (assume the mass of the top is related to the W and Z), and then the number of degrees of freedom of the fermionic sector is 2*36.

MTd2

Sorry, I just noticed that it is the default name for any moviment I can make.

yoyoq

so...how was lunch with distler?
what did you guys eat?
who paid?
how much of a tip did you leave?

MTd2

Garrett,

Yoyoq,

I posted your question here!!!:


http://golem.ph.utexas.edu/category/...n.html#c018769

rntsai

a year later...any progress on finding a way to fit three generations into e8?

Berlin

Maybe the best strategy for E8 fans would be to accept the fact that only one generation fits into the full E8! That is, I think, not as strange as it looks. In fact, the three generations are only distinguishable in mass (and could so, be identical in the mass to zero limit). Having three doublets of Higgs could cause three different mass levels only after breakdown of some of the E8 symmetries. See it like the only true generation is stuck in three different potential wells (maybe even combined with a Pauli principle). I am trying to use a kind of trinification model based on SU(2)^3, breaking down to three left SU(2)xSU(2)xU(1) groups with a left-right symmetry breaking a la Senjanovic. One of these left SU(2) groups should be part of gravity, the rest is EW. Only the 128 spinor "1/2" states of E8 seems to be required for the fermions. Whether this means that even gravity only exists in its current form after a symmetry breaking I do not know (or that the very notion of left-right comes along at that moment). All crazy ideas and the maths turns out too difficult for me anyway. Fun though.

berlin

CarlB

On the generation structure, Marni Sheppeard and I have been working on a method of describing it based on (my view of things may differ from hers) the discrete Fourier transform. Partly to justify this, I've applied the same theory to the hadrons and have found 39 equations relating their masses.

This is similar to Regge trajectories (which were used as the basis for string theory). Regge trajectories are equations that relate the masses of the same hadrons but with different angular momenta. The equations I've got relate the same hadrons but with different radial excitations. But it attributes the different radial excitations to color phase effects.

I'm submitting this to Phys Math Central next week and would appreciate comments on it:
http://www.brannenworks.com/koidehadrons.pdf

As far as E8 theory goes, this would mean something like E8 x discrete Fourier transform for the generations.

MTd2

Hi Carl,

Have you contacted Garrett Lisi about this? He could surely help you. Also, he colaborated intesively with Lee Smolin. I would like to know what you would talk to them, if you are willing to. You should also ask Tommaso Dorigo.

MTd2

Another question,

I really really expected to see the top mass calculated with you method... I know, everything else is really awesome, but I am disapointed with this one...

CarlB

Another example of a cute theory that only gives one generation of the elementary fermions, see:

Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation

Piotr Zenczykowski.

According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.
http://arxiv.org/abs/0901.2896

So does the above have anything to do with the way Garrett packs a single generation into E8? I don't think so but others understand his theory better than me.

P.S.

MTd2, when I had done this originally, it was based on assumptions which violated special relativity. That probably put Smolin off his feed. The latest version hides all that stuff by sticking to quantum information theory (where position and momentum are ignored, hence there is no need for special relativity or a replacement for it) and so that might get by better.

I seem to have given it an attractive abstract because some important people have written to me saying that they are very busy, especially this time of year, but they are going to take the time to read the paper. I think that basically, it's an attractive way of extending Regge trajectories to radial excitations and I wonder if I should give it a title that mentions Regge trajectories instead of Koide mass formulas. Hmmm.

rntsai

I quickly read through this and I'm afraid I don't
see the main point. It looks like you take these
masses three at a time and find a data fit for them
using three real parameters. You use 3x3 circulant
matrices to inspire the form of this fit. These matrices
(and their eigenvalues) are defined by 3 parameters.
It's well known that all circulant matrices (any size)
are diagonalized by the discrete fourier transform matrix,
so they will all have the same eigenvectors; I don't think
that adds anything. At the end, it's still just a fit of 3
numbers by three parameters. It doesn't look like there's any
relation between the different fits...each has it's own
set of 3 parameters (right?). It's also not apparent how
special these fits are. It seems there are enough degrees
of freedom to fit any randomly picked 3 numbers to this
form...

CarlB

Thanks for reading! You are right that this is the effect of the discrete Fourier transform; it takes three real variables and turns them into three real variables (or one real variable and one complex variable). Whichever, it keeps 3 real degrees of freedom. But read on.

No, there are only two parameters for each fit, "s" and "v". You're probably confused by the constant that is in front of each fit. This is a constant equal to 25.054 square root MeV and is not a parameter. It's value never changes. It's taken from the electron fit.

If it still isn't obvious that there are only two degrees of freedom, note that multiplies s and v. So you could define

and get each fit down to two real parameters.

By the way, you're not the only one to make this error. When my neutrino paper came out a few years ago it used similar notation and I had a professor of physics tell me that it used 4 parameters, LOL. It must be a natural mistake on a fast read. I've got the factored out because it's a natural scale.

By the way, if I had 3 real parameters to play around with, I wouldn't have errors, LOL. The third parameter becomes the angle delta. The claim is that the mass spectrum can be closely approximated by quantizing delta as or

I wouldn't be surprised if other people make the same error, but I don't think I'm going to eliminate the scale factor. From a sociological point of view, a paper that has not passed peer review gets read by people who don't expect anything good and really don't pay very close attention to the details. So they reject things as soon as they find the first detail that disagrees with them. But after a paper is past peer review this effect should go away.

MTd2

Garrett has some new ideas. Jacques Distler couter argues:

http://golem.ph.utexas.edu/category/...t.html#c022012

arivero

http://www.slac.stanford.edu/spires/...RXIV:0711.0770