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Permanent magnets.
...If we put a piece of iron in a strong magnetic field, when this inducing magnetic field is cut, this metal will keep a permanent magnetization. Why?
...The magnetic field acts on the spins of electrons, which behave like mini-magnetic dipoles, mini-magnets. But why do they keep the orientation imposed by the inducing field, after this one is cut?
...Because electrons are like Panurge's sheep. Each one follows the field due to its neighbours. Then they all keep their parallelism. This order can be destroyed if one warms or hammers the metal.
The magnetic momentum of anti-matter.
...The charge conjugation reverses the gyromagnetic coefficient, in the Dirac's antimatter. Then the spin s being unchanged but it reverses the magnetic momentum of the particle.
Notice this matter anti-matter symmetry does not change the energy E, nor the particle's impulsion p.
The four components of the Lorentz group.
Above, we presented that we called the "PT-group", a four components ruling the P, T and PT symmetries.
(300)
Then was presented the Galileo group "space and time oriented".
(301)
Then was presented the complete four components Galileo group.
(302)
with P, T and PT symmetries.
The Lorentz group element (4,4) L obeys the axiomatic definition:
(303)
(304)
L acts on space time:
(305)
Like the Galileo's complete group the complete Lorentz group has four components:
Ln elements: keep space and time orientation unchanged.
Ls elements: achieve space inversion (P-symmetry)
Lt elements: achieve time-inversion (T-symmetry)
Lst elements: achieve space and time inversion (PT-symmetry)
Give an example of matrixes which belong to the four components:
(306)
An = 1 (neutral element) 
Ln keeps space and time unchanged
As Ls inverses space.
At Lt inverses time.
Ast Lst inverses space and time.
The neutral component is a sub-group of the complete Lorentz group.
Remark:
(307)
At = - As
Ast = - An
Two component form a sub-group:
(308)
Lo = Ln U Ls
whose elements do not reverse time. Souriau calls it the orthochron sub-group Lo of the complete Lorentz group L. The rest of the group, the set of matrixes which belong to the third and fourth components:
Lac = Lt U Lst
do not form a group but a set of matrix, that Souriau calls antichron set. Then the complete Lorentz group is (U for "union")
(309)
L = Lo U Lac
But, writing
(310)
m Lo, avec m = ± 1
we get the complete group.
The four components ofthe Poincaré's group.
From the Lorentz group one builds the Poincaré's group:
(311)
C being the space-time translation vector:
(312)
...The complete Poincaré's group owns four components, due to the four components structure of the Lorentz Group. In classical physics the Poincarés' group is limited to its neutral component.
...We have built in preceding sections the coadjoint action of the group on its momentum's space, which works "in general", whatever the chosen component is. In the following we examine the action for the different components. This was done earlier by J.M.Souriau:
Souriau, Structure des Systèmes Dynamiques, Dunod 1973, in french, andBirkhauser Ed. 1997, in english, chapiter III, page 197, in a section entitled: Inversions of space and time.
