THE DYNAMIC GROUPS OF PHYSICS

• Dynamic groups of physics
  
  Table of contents:
  
   
  1. General points. Axioms of group theory.
  2. General points. Dimension of a group. Group's action.
  3. The first groups of matrixes. Translation. Rotation. Sub-groups. Species.
  4. Orthogonal matrixes. Orthogonal groups.
  5. Symmetries.
  6. Components of a group. The Euclid's group.
  7. Orthogonal group O(3)
  8. Following calculation.
  9. About components of the group. Extension to 4d PT-group.
  10. Following calculation.
  11. Mirrors. "PT-theorem"
  12. A parenthesis: Space-time orientation.
  13. The Galileo groups. Movements. Momentum.
  14. Coadjoint action of a group on its momentum space. What is physics?. Actions.
  15. Following calculation.
  16. Dual actions. Towards building the essential action, or coadjoint action of a group on its momentum
  17. Choice of the matrix m. Coadjoint action of the Poincaré group on its momentum space.
  18. Following calculation. Matrix representation of momentum.
  19. The spin, a geometrical object. Evocation of the coadjoint action of the Bargmann group.
  20. "Passage" cancellation in the matrix description with a coordinate change. The photon.
  21. The neutrino. Non zero particles with spin.
  22. The four components of the Lorentz group.
  23. Orthochron and antichron components of the Poincaré group.
  24. The Galileo group. Trivial extension of the Galileo group.
  25. Non-trivial extension of the Special Galileo's group. The Bargmann's group. Central extension of the Poincaré group.
  26. Particles and antiparticles' zoo.
  27. A geometrical definition of antimatter.
  28. Geometric description of Dirac's antimatter. Geometric description of Feynman's antimatter.
  29. CPT theorem. Action on Photons.
  30. Considered solution.
  31. About the contents of the two folds. The twin group.
  32. Some comments about the metrics. Interacting folds. Conclusion.