> 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
> "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 )
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.