The proposal has profound consequences. One might say that SUSY in the TGD sense has been below our nose for more than a century. The proposal could also solve matter-antimatter asymmetry since the twistor-lift of TGD predicts the analog of Kähler structure for Minkowski space and a small CP breaking, which could make possible a cosmological evolution in which quarks prefer to form baryons and antiquarks to form leptons.
The basic objection is that the leptonic analog of Δ might emerge. One must explain why this state is at least experimentally absent and also develop a detailed model. In the article Can one regard leptons as effectively local 3-quark composites? the construction of leptons as effectively local 3 quark states allowing effective description in terms of the modes of leptonic spinor field in H=M4× CP2 having H-chirality opposite to quark spinors is discussed in detail.
See the article Can one regard leptons as effectively local 3-quark composites? and the chapter The Recent View about SUSY in TGD Universe.
For a summary of earlier postings see Latest progress in TGD.
5 comments:
According to this idea, p and e are both made of uud. But what is the actual difference between p and e, then?
The total quantum numbers of p and e^+ are same (recall that TGD color differs from QCD color in that color is angular momentum like, not spin-like and the colar partial waves has color representations correlation with em charge: tjhis is essential).
There are following differences.
a) The quarks in p are at different partonic 2-surfaces with distances of order proton size scale. This makes possible strange, charmed etc variants of baryons. The quarks in e areat the same partonic 2-surface with size of order 10^4 Planck lengths, the CP_2 size scale. For leptons one has only different generations corresponding to genus of the partonic 2-surface.
b) The color representation of U quarks are triplets but those of D quarks are not. The color wave functions of each D quark in proton is reduced to triplets by acting with super-Kac Moody type generators which are color octets. The super-Kac-Moody generators also increase the conformal weight to zero (masslessness). which is in general negative due to negative vacuum conformal weight.
In the case of e color neutralization is not carried out separately for quarks but for the entire 3 quark state.
c) For baryons the wave function in spin-isospin degrees is totally symmetric since color is antisymmetric (statistics).
For electron this could be also true. For neutrinos the color and spin-ew degrees of freedom must entangle since color wave function is not singlet antisymmetric under exchange of quarks.
I apologize in advance for my insufficient understanding of TGD. I have a simplified mental model of TGD which is probably wrong, hopefully you can correct me.
The simplified mental model is that for the color interaction, we have punctured 2-surfaces somehow interacting with modes of the CP_2 metric. The punctures are the quarks and SU(3) would come in the usual Kaluza-Klein way.
In terms of this model, the difference between proton and electron would be, that proton contains three 2-surfaces each with one puncture, while electron is one 2-surface with three punctures.
I have many other questions. But first I need to correct this mental picture!
I just remembered that in string theory, one doesn't get the forces in "the usual Kaluza-Klein way". So probably that isn't what happens in TGD, either!
Your view about baryons and leptons is correct. I answered already early or at least wrote the answer. Sorry for slowness.
*Only color interaction is analogous to Kaluza-Klein.
*Electroweak connection is projection of CP_2 spinor connection. Bundles induction is standard notion but colleagues have not found it for some reason. Stringy picture is different: the gauge fields emerge by spontaneous compactifications.
* In TGD standard model gauge potentials and gravitational field emerge when many-sheeted space-time is replaced with slightly curved region of Minkowski space. Standard model gauge potentials are sums of components of spinor connection for sheets and projections of Killing vectors of SU(3).
*At M^8 level local color gauge group emerges as a subgroup of G_2 acting as octonionic automorphisms. Co-associativity condition for space-time surfaces implies that space-time surface is obtained by local G_2 transformation acting on flat M^4. SU(3) gauge potentials do not reduce to gauge.
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