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. (p3)
...Two more sectors have to be
explored. On the third we examine the impact of ( l
= - 1 ; m = - 1 ) element
on the momentum and movement.
...( l
= - 1 ) reverses the {zi}. According to our geometric definition this new movement corresponds
to antimatter, for it takes place in the second sector of space { z1 ,
z2
, z3
, z 4
, z 5
, z 6,
x, y , z , t }.
( m
= - 1 ) gives a PT-symmetry, reverses the signs of ( x, y , z , t )
...But ( l
m = + 1 ) keeps the charges unchanged. This is "PT-symmetric
antimatter", so that it is a geometric description of antimatter after Feynmann.
...But the group belongs
to the antichron sector, so that (coadjoint action) the energy and the mass
of the particle is reversed.
...PT-symmetrical object
does not identify completely with Dirac's antimatter, for it changes the sign
of the mass. If such particles exist, they can produce full annihilation with
positive mass particles.
.
Fig. 6 : ( l=
-1 ; m = -1 ) elements
transform movement of normal matter into movement of antimatter (z-Symmetry)
of PT-symmetrical object, runing bacward in time.
Geometric description of Feynmann's vision of antimatter.
Does not identify vompletely with Dirac's one : negative
mass and negative energy.
The last elements correspond to the sector ( l=
1 ; m = -1 )
( l =
1 ) --- > the movement is still in the matter's sector :
no z-Symmetry.
( m
= -1 ) goes with a PT-symmetry. The particule runs backward in time.
( l
= -1 ) : C-Symmetry. The charges are reversed.
...This is CPT-symmetrical
matter, so that it corresponds to a geometrical interpretation of the so-called
"CPT theorem", which asserts that the CPT-symmetric of a particle should be
identical to that particle. That's not true. This movement corresponds to
an antichron movement. The particle goes backward in time, si that (caodjoint
action) its mass and energy become negative .
If CPT-symmetrical particle do exist and if they collide
normal particle, complete annihilation occurs.
.
Fig.7 : ( 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 particule
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 a 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 keep unchanged its energy. See figure 8.
.
Fig. 8 : Coadjoint action
of orthochron elements
on photon's movement and moment.
.
Fig.9 : The coadjoint
action of antichron elements on photon's movement and moment,
reverses the photon energy : it travels backwards
in time.
