Geometrization
of matter and antimatter through
coadjoint
action of a group on its momentum space. 4 :
The
Twin group. Geometrical description of Dirac's antimatter.
Geometrical interpretations of antimatter after Feynman and so-called CPT-theorem. (p3)
The movement of a particle which is the CPT-symmetrical of a normal particle takes place in the fold F*.
.
Fig.7
(45f7)
:
( l
= 1 ;
m
= - 1 )
case. Corresponds to CPT-symmetry.
But the coadjoint action gives negative mass and energy.
The CPT-symmetric of a particle of matter is a particle of matter, but with negative mass.
Now, examine the impact on photons movement and moment. The
z-
Symmetry has no impact on it : there is no "antiphoton". As all the charges of the photon are zero it does not change it. It is identical to its antiparticle.
The coadjoint action of orthochron components modifies the movement and the moment of the photon, but keeps unchanged its energy. See figure 8.
.
Fig. 8
(45f8)
: Coadjoint action of orthochron elements
on photon's movement and moment.
.
Fig.9
(45f9)
: The coadjoint action of antichron elements on photon's movement and moment,
reverses the photon energy : it travels backwards in time.
The antichron elements of the group acts on the momentum through coadjoint action. Such elements transform the normal photon, travelling forward in time in the
z = 0 plane of the fold F into a movement in the corresponding plane of the fold F*. This photon travels backwards in time. Its energy is negative.
About the contents of the two folds.
They can be summarized in the following tables.
.
Fig.10
(45f10)
: Classical particles-antiparticles zoo.
.
.
Fig.11
: Ghost particles-ghost-antiparticles zoo.