### A comment about exact Yangian symmetry realized in terms of bound states of partons

The formulation for the earlier view about how bound states allow to realize super Yangian (and super-conformal symmetry) was not yet quite correct. The correct formulation is extremely simple.

- The condition is that the total super momentum for the bound state must have a vanishing super part. Note that for single parton states it is satisfied only by putting super-momentum component to zero by hand, which looks somewhat strange. In TGD framework all observed particles are bound states of partons assignable to wormhole throats.
- Since super-momenta are quadratic in super-spinors λ this gives a linear constraint on super-parameters of form X= ∑ λ
_{i}η_{i}=0 , where the sum is over the partons forming the bound state. A condition of same form follows from the condition that external super-momenta sum up to zero for scattering amplitudes: in this case one could say that one has zero energy bound state with S-matrix or its generalization to M-matrix giving the entanglement coefficients. - The action of the super-components on the total (super-) momentum p= ∑λ
_{i}λ*_{i}(here * refers to tilde) appearing as argument of the scattering amplitude gives something proportional to these quantities and therefore vanishes. Hence bound state property and non-locality is essential for having super-conformal invariance and also IR cutoff since the mass of the bound state brings in the mass/length scale.

## 6 Comments:

"the total super momentum for the bound state must have a vanishing super part." - could this be as instance the higher families of fermions? They are like scaled up variants of ground state,

"that external super-momenta sum up to zero for scattering amplitudes: in this case one could say that one has zero energy bound state with S-matrix or its generalization to M-matrix giving the entanglement coefficients." - this is ground state with a minimum energy?

If antimatter vanish with time then as instance sensory experiencies always happen in past times, that is in antimatter (memory). Can this be the right explanation? Also oscillations can be said to be a connection between past times and present times; between antimatter and matter.

"Hence bound state property and non-locality is essential for having super-conformal invariance and also IR cutoff since the mass of the bound state brings in the mass/length scale." - How is this depending on time?

Super-space is highly formal notion which many mathematicians and also physicists refuse to take quite seriously. It is however extremely practical tool and leads to the notions like super-momentum. Super part of the super momentum is not ordinary number: for instance x^2=0 for any super number and this is obviously something strange.

If one however takes super-momentum seriously as a formal tool (TGD does not require but allows this) one can say that for real physical particles the super part of momentum must vanish. This I claim to have the highly desired implication that one can have exact super-conformal invariance, non-trivial scattering amplitudes, and no infrared divergences.

The physical assumptions are of course more important than formalism used to express them: observed particles as bound states of partons identified as wormhole throats carrying fermionic quantum numbers and with light-like momenta summing up to massive total momenta.

"for real physical particles the super part of momentum must vanish"

The momentum would vanish if position is found. However, position is found only if space is expanded enough to break the symmetry. What are real physical particles? This is relative to space we observe, but space is defined if mass existed constantly in a zero, thus condensates are observed when spin is decreased to the extend where particles interfering as independent systems would stop generating waves as strings will shorten. Strings connect temporally waves and particles because antimatter has a broken symmetry. This is why leptons have different mass and potential. Zero is a hole through which new boundary states are found, therefore time is a n-dimensional "super" dimension, which can lead you to endless quantum world, due to its discontinuity while interfering with matter.

The notion of real particle is theory dependent. Real particles are mathematical entities which have the quantum numbers of particles we measure in lab. The challenge is to understand how the fundamental objects (say strings) form the physical particles and show that theory allows them.

Even in standard model the bridge from quarks to hadrons is poorly understood.

If you want to make superstring theorist to blush and stumble in his words, ask him how he understands atom in terms of strings. Actually even electron is enough!;-) They do not have yet this kind of correspondence which is of enormous help for a theorists trying to wade his way from dreams to the reality and to tell the layman for what purpose his theory is useful;-).

In TGD framework situation is rather satisfactory since one of the starting points of theory was the idea about this correspondence in terms of symmetries.

The idea about time as multi-dimensional leads to obvious difficulties with what we know about geometric time. I also think that we would experience geometric time as multidimensional if it really were multi-dimensional since an approximate correspondence between geometric and subjective time looks natural.

Mass compactification.

From: http://blog.vixra.org/2010/09/21/quark-gluon-plasma-seen-in-proton-collisions-maybe/#comment-4222

I believe Wilzcek commented that the reason gravity is so weak is that the masses of particles are so small [=zero]. I make a phys-101 argument below on masses and compactification, The mass is m ~ 1/r, for r the radius of compactification. If this is near the Planck or string scale these masses would be enormous [=mass change]. This is one motivation for large extra dimensions. [Lawrence Crowell]

Could you please comment on this and the connection to your mass hierachy at the Planck scale?

In my personal Universe CP_2 size defines the fundamental length scale and therefore also the fundamental mass scale as its inverse. The weakness of gravitation is due to the smallness of this scale. This scale is not Planck length but about 10^3-10^4 times longer scale, roughly the unification scale of GUTs.

The small mass of observed particles results from p-adic thermodynamics. The thermal mass squared resulting from thermodynamics for Virasoro generator L_0 scales are predicted to come as m^2(CP_2)/p where p is the p-adic prime characterizing the particle. This not the only source of mass but the argument about scale holds true.

The large values of the p-adicprimes p explain the smallness of the thermal mass squared.

For instance, for electron one has p= 2^{127}-1=about 10^{38}, the largest Mersenne prime for which p-adic length scale is not completely super-astrophysical.

A very powerful prediction of p-adic length scale hypothesis stating that p =about 2^k, is that mass scales come as half octaves. There is empirical evidence that particles can appear also as scaled up variants.

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