Chirality and Symmetry Breaking in a Discrete Internal Space
Abstract
In previous papers the permutation group S 4 has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S 4 is the pyritohedral group A 4× Z 2 because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S 4→ A 4. Since A 4 is a chiral group, while S 4 is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.
- Publication:
-
International Journal of Theoretical Physics
- Pub Date:
- October 2012
- DOI:
- 10.1007/s10773-012-1190-y
- arXiv:
- arXiv:1201.2281
- Bibcode:
- 2012IJTP...51.3073L
- Keywords:
-
- Quarks;
- Leptons;
- Tetrons;
- Magnon;
- Phonon;
- Phase transition;
- Nonabelian;
- Generation symmetry;
- Family symmetry;
- Symmetric group;
- Permutation group;
- Mass matrix;
- Chirality;
- Parity violation;
- Grand unification;
- Higgs mechanism;
- Spontaneous symmetry breaking;
- Compactification;
- Discrete symmetry;
- Internal crystal;
- Internal molecule;
- Spin model;
- Emergent gauge theory;
- Heisenberg model;
- High Energy Physics - Phenomenology
- E-Print:
- 42 pages, 3 tables