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Neutrinos.
...Considered as zero-mass particles (which they are, until someone provides evidence of their mass), neutrinos have momentum matrices similar to those of photons. But their spin is 1/2.
(293)
...Neutrinos move at the speed of light. They possess a quantized spin, different from that of the photon. We know that there are three different kinds of neutrinos (electronic, muonic, tauonic). But the Poincaré group is unable to account for this distinction in terms of new geometrical features. To do this, we will be obliged to include charges in the momentum. For neutrinos we have three different charges:
cL = leptonic charge = ± 1
cm = muonic charge = ± 1
cn = tauonic charge = ± 1
...Charge inversion corresponds to matter-antimatter duality (after Dirac). It is called charge conjugation or C-symmetry.
Then the three neutrinos each have their own antiparticle, which corresponds to:
(295)
Non-zero particles, with spin.
Then there is no longer a link between energy and momentum:
(296)
Calling m the "rest mass", we can write:
(297)
(297b)
Limit our classification to:
Proton
electron
neutron
and the corresponding antiparticles.
...These particles possess different attributes, called charges, which do not come from the Poincaré group, as geometrical attributes.
There are:
-
Electric charge e = ± 1
-
Baryonic charge cB = ± 1
-
Leptonic charge cL = ± 1
-
Muonic charge cm = ± 1
-
Tauonic charge ct = ± 1
-
Gyromagnetic coefficient v (positive or negative)
...The inversion of all these quantities (charge conjugation or C-symmetry) corresponds to the matter-antimatter duality (after Dirac). To sum up:
(298)
(298b)
which can have any direction. The magnetic moment, the spin vector s and the gyromagnetic factor v are linked through:
(299)
...Here we used a bold letter to describe the spin vector, which can point in any direction in space. But its length is quantized. C-symmetry (charge conjugation) reverses the charges, the gyromagnetic factor v, but not the spin. Thus it reverses the magnetic moment of the particles.
