a4129

Consider now a component ( l = - 1 ; m = - 1 )
(396)

( l = -1 ; m = -1 ) elements transform movement of normal matter into movement of anti-matter (z-Symmetry) of PT-symmetrical object, runing backward in time. Geometric description of Feynmann's vision of anti-matter. Does not identify completely with Dirac's one : negative mass and negative energy.

We get Feynmann anti-matter. But, as pointed out by Souriau in 1973, a PT-symmetrical particle goes backwards in time. Its mass and its energy are negative.

Remark : in this description the fact that the movement corresponds to positive or negative energy element does not appear in the evolution space (top-left).

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.
(397)

( 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.
(398)

Coadjoint action of orthochron elements

on photon's movement and moment.

(399)

The coadjoint action of antichron elements on photon's movement and moment, reverses the photon's energy : it travels backwards in time.

...We see that reintroducing antichron components in the group arises PT-symmetric anti-matter and CPT-symmetric matter. Both go backwards in time. Both come from the action of an antichron element of the group on a normal matter movement. Anti-matter is nothing but a peculiar movement . Same thing for CPT-symmetrical matter which cannot be any longer identified to normal matter, as classically asserted by so-called CPT-theorem, for the mass of a particle which is CPT-symmetrical of a normal matter particle owns negative mass and negative energy.

Similarly the Feynmann antimatter owns a negative mass and nbegative energy ( while the Dirac's antimatter own positive mass and energy ).

Index Dynamic Groups Theory