Chirality and Symmetry Breaking in a discrete internal Space

Details Chirality and Symmetry Breaking in a discrete internal Space Chirality and Symmetry Breaking in a discrete internal Space

2012-01-11

arxiv.org/abs/1201.2281v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

42 pages, 3 tables

Scientific paper

In previous papers the permutation group S_4 has been suggested as an ordering scheme for elementary particles, 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 x 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.

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