Geometrization
of matter and antimatter through
coadjoint
action of a group on its momentum space. 3:
Geometrical
description of Dirac's antimatter.
A
first geometrical interpretation of antimatter
after Feynmann and
so-called CPT-theorem. (p4)
Conclusion.
...We
have extended the group, including antichron elements. We refind the geometric
description of Dirac's antimatter. But the analysis of the coadjoint action
of antichron elements of the group produces PT-Symmetrical and CPT-symmetrical
movements.
...We find that PT-symmetry goes with matter
-----> antimatter transform. It joins Feynmann's idea. The PT-symmetric of
a particle of matter is a particle of antimatter. But the coadjoint action
of antochron elements reverses the mass and the energy. Then we cannot identify
the PT-symmetrical of a particle of matter to its antiparticle, after Dirac's
description.The first owns a negative mass and a negative energy.
...Similarly the CPT-Symmetric of a particle
of matter is a partocle of matter, but with a negative mass, for it goes backwards
in time.
...The problem remains unsolved. As recommanded
by J.M.Souriau, we could limit the dynamic group to its orthochron part, but
we would'nt have PT and CPT-symmetrical object for symmetries including time-symmetry
becomes forbiden.
If we keep the antichron sector we have an universe filled by positive and
negative mass particles.
Charybde or Scylla.?
In the next paper we shall propose another solution.
References.
[1] J.P.Petit & P.Midy : Geometrization of matter and antimatter through
coadjoint action of a group on its momentum space. 2 : Geometrical description
of Dirac's antimatter. Geometrical Physics B, 2 , march 1998.
[2] J.P.Petit & P.Midy : Geometrization of matter and antimatter through
coadjoint action of a group on its momentum space. 1 : Charges as additional
scalar components of the momentum of a group acting on a 10d-space. Geometrical
definition of antimatter. Geometrical Physics B, 1 , march 1998.
[3] J.M.Souriau : Structure des Systèmes Dynamiques, Dunod-France Ed.
1972 and Birkhauser Ed. 1997.
[4] J.M.Souriau : Géométrie et relativité. Ed. Hermann-France,
1964.
[5] P.M.Dirac : "A theory of protons and electrons", Dec. 6th 1929, published
in proceedings of Royal Society (London ), 1930 : A 126 , pp. 360-365
[6] R.Feynman : "The reason for antiparticles" in "Elementary particles and
the laws of physics". Cambridge University Press 1987.
Acknowledgements.
...This work was supported by french CNRS and
Brevets et Développements Dreyer company, France.
Déposé sous pli cacheté à l'Académie des
Sciences de Paris, 1998.
Copyright french Academy of Science, Paris, 1998.
