Natural Science Forum / Physics / Particle Physics / October 2005

Hi Adron,

I know that Bjoern started a university teaching position last month as well
as moved, so he may have his hands full with other things.

I actually think all of the elementary fermions contain two internal
symmetries: one is the STRONG leptoquark symmetry which gives a fermion one
of three colors or a lepton number; the other is WEAK isospin symmetry which
makes a fermion either isospin up or isospin down.  This is the most elegant
way to account for the "redundancy" wherein both quark and leptons have weak
isospin.  That is, I believe the isospin redundancy is a very direct
indicator that the internal symmetries of the elementary fermions are
leptoquark color, and isospin up and down.  WEAK isospin is a redundancy of
STRONG leptoquark symmetry; while the STRONG symmetry of leptons and quarks
at high energy is a redundancy of WEAK isospin and this is where weak and
strong interactions end up being joined at the hip with a WEAK isospin and a
STRONG leptoquark "preon."  Look at section 12.2 in Volovik for details; I
agree with everything there, except for the holon / spinon stuff which, back
in my days at M.I.T., we used to call a "kludge" (maybe they still do, some
things at the 'tute don't change.)  The holon / spinon stuff is an
inelegant, and, I believe, merely interim way of dealing with the spins
pending something more compelling.

Spin, of course, is a symmetry emanating from spacetime, as opposed to the
internal symmetries that arise from the generators of Yang Mills / Lie
algebras.  The additional degrees of freedom that come about from having
magnetic-type charges in addition to electric-type charges actually allow us
to use everything in Volovik section 12.2 regarding internal symmetry, and
also to give spin 1/2 to each of the holons and the spinons, and to have the
composite particle that they form ALSO be spin 1/2.  That is, we all learned
that 1+1 = 2, but here, we can actually arrive at 1/2 + 1/2 = 1/2.  I spent
over 20 years trying to figure out how to do this once I realized that the
weak isospin redundancy lends itself to a preonic decomposition of the
fermion, and now I have found that the magnetic monopoles are the key to
this and in particular the chiral connections in
http://arxiv.org/abs/hep-ph/0509223 are the starting point for this
development.

I will develop this in detail in a future paper, but this funny 1/2 + 1/2 =
1/2 arithmetic actually has it basis in the Weyl representation of the Dirac
equation.  Briefly, as is well-know, one can "add" a left-handed massless
spin 1/2 fermion f_L to a right handed massless spin 1/2 fermion f_R to
still arrive at a spin massive 1/2 massive f = f_L _ f_R, and insofar as the
spins go, we have applied 1/2 + 1/2 = 1/2 due to the unique algebraic
characteristics of the Dirac matrices which I regard as the "generators" of
spacetime symmetry much as, for example, the Pauli matrices are the
generators of SU(2) internal symmetry of the Gell Mann matrices are the
generators of SU(3).  (This also leads me to the view that the Dirac gamma-5
is a direct indicator of a fifth, timelike, axial spacetime dimension and
that time is therefore a plane not a line and that the observed mass of a
particle depends on how it travels through the time plane relative to how we
travel through the time plane, and that Feynman's discovery that particles
can travel "backward" through time -- essentially defining an
antiparticle -- should be extended to particles being able to travel
sideways through time (for a massless particle) or at an "angle" through
time (for a massive particle), but that too, is another full paper.)

As it turns out, the findings in http://arxiv.org/abs/hep-ph/0508257 and
http://arxiv.org/abs/hep-ph/0509223 regarding magnetic monopoles, once
applied to weak and strong interactions, allows the Fermions to be composed
out of Volovik's holons and spinons, but also allow each of these to have
spin 1/2 because of the 1/2 + 1/2 = 1/2 arithmetic of the Dirac matrices
based on the connection between chirality and magnetic monopoles developed
in http://arxiv.org/abs/hep-ph/0509223.  This all takes place through an
elegant mathematical conspiracy involving all of a) weak isospin and strong
leptoquark internal symmetry, b) the (broken) duality symmetry of electric
and magnetic charges, and the c) chiral properties of Dirac's gamma
matrices.

And somewhere in the middle of all this, though have not yet nailed it in
detail, is, I believe, a resolution to the Fermion mass problem, that is,
the question of why the fermions have the masses they have.

Jay.