5-bit coding of the fermions
Carol von der Lin
fully classifies a generation of the Standard Model fermions.
It is a "plus-minus" code based on a spinor representation of
SO(10). Details can be found in Zee's new book "Quantum Theory
in a Nutshell" p. 410 ("A binary code for the world.") We wish
to report a kindred 5-bit coding scheme of our own, this of
"on-off" type, that finds its natural interpretation in the
finite projective space PG(4,2). We should like to know if this
has already been reported elsewhere. The best way to see what it
is about is on two pages on a website dedicated to
another purpose: http://www.kashmirstamps.ca/01projective.html
Best regards, Carol von der Lin in Canada.
Alfred Einstead
vond...@hotmail.com (Carol von der Lin) wrote:
> F. Wilczek has reported an intriguing 5-bit register that
> fully classifies a generation of the Standard Model fermions.
> We should like to know if this has already been reported
> elsewhere.
"The Particle Spectrum Is On A Regular 5-D Simplicial Grid"
s.p.r., January 16, 2003
"The Particle Spectrum On A 6-D Cartesian Lattice"
s.p.r., January 20, 2003
"The 6-D Particle Lattice"
s.p.r., October 29, 2003
"6-D Particle Lattice & Regularities In Particle Spectrum"
s.p.r., November 9, 2003
The regularity is this: the following 5 quantum
numbers take ONLY the values +1/2 and -1/2 for the
fermions; and take ALL 32 combinations of these values,
if the right neutrinos and left anti-neutrinos are
counted:
a = -(B-L)/2 + Y/g' - I3/g
b = -(B-L)/2 + Y/g' + I3/g
c = (B-L)/2 - L8/(sqrt(3) gs) - L3/gs
d = (B-L)/2 + 2L8/(sqrt(3) gs)
e = (B-L)/2 - L8/(sqrt(3) gs) + L3/gs
where (B-L)/2 = 1/2 (Baryon - Lepton), Y = weak
hypercharge (with right-electron = -g'), I3 =
weak isospin (left-electron = -g/2), L3 and L8
the SU(3) casimir charges; g', g and gs the
U(1)_Y, SU(2)_W and SU(3)_{color} coupling constants.
The quantum numbers take on the values +1 and -1 for
the charged vector bosons, and take on 8 of the 20
+1/-1 possible pair combinations.
The 4 modes of the Higgs take on the 4 combinations
of +1/2 and -1/2 for two of the qubits.
The inverse relations (listed in the November 9 article)
are:
Y = g' ((a+b)/2 + (c+d+e)/3)
I3 = g (b-a)/2
L3 = gs (e-c)/2
L8 = gs (-c+2d-e)/sqrt(12)
(B-L)/2 = (c+d+e)/3
Carol von der Lin
whop...@csd.uwm.edu (Alfred Einstead) wrote in message news:<e58d56ae.03112...@posting.google.com>...
> "The Particle Spectrum Is On A Regular 5-D Simplicial Grid"
> "The Particle Spectrum On A 6-D Cartesian Lattice"
> "The 6-D Particle Lattice"
> "6-D Particle Lattice & Regularities In Particle Spectrum"
Thanks for the references! A sleek and variously
suggestive story seems to emerge at the lower 3-d and
4-d levels in the finite projective-space language.
Had wondered in the original question if anyone had
published the projective angle; I suspect that more
than a few have noticed such systematics over the years,
if only for its considerable, if slightly alarming,
mnemonic or pedagogic virtues.
( http://www.kashmirstamps.ca/02projective.html )
Alfred Einstead
> over the years, if only for its considerable, if slightly alarming,
> mnemonic or pedagogic virtues.
Note the difference, however. The only way to get the vectors
mentioned therein to line up 60 degrees apart from each other
is for (+++++) and (-----) to be assigned to the right electron
and left positron; not the right neutrino and left anti-neutrino.
ise...@lmc-vo.nl
Your page http://www.kashmirstamps.ca/01projective.html is not available
any longer. Few years ago, I have seen this page and printed it. Now I
am preparing an article to be possibly published in a scientific journal
and would like to make a reference to your work. Is it possible?
Thank you in advance,
Best regards,
I.V. Serov
[Moderator's note: I'm not sure where the quote above comes from, nor
whether Carol von Der Lin reads the group here; if so, perhaps they can
respond. Note that http://www.kashmirstamps.ca can now be found at
http://www.kashmirstamps.com, though not without the page on physics
mentioned above. The website is about stamp collecting, which of course
doesn't rule out the fact that some physics page might have been there
at some point. I'm reminded of Ernest Rutherford's quip: "Science is
divided into two categories, physics and stamp-collecting." -P.H.]