Tetron Model
The Tetronmodell is the attempt to attribute the observed quark and lepton 24 - Flavors and their interactions in a more simple structure. It is based on the structure of the permutation group S4, according to their representations, the quarks and leptons (and also the vector boson states) of the standard model may be applied ( see graph).
A possible explanation of this classification scheme was proposed by Bodo lamp. It consists in the assumption that the area of internal symmetries is not continuous, but a three-dimensional lattice with tetrahedral symmetry (which is isomorphic to S4 symmetry group). The observed particles can be interpreted as comments on this grid, characterized by the representation of the lattice symmetry group.
Statement in higher dimensions
It then automatically switches the question of the origin has the discrete inner S4 symmetry. To answer this question, in a ref ( flukturierendes quantum ) lattice viewed in a (6 1 )-dimensional space-time ( eg with S8 as a symmetry group), the symmetry is broken, so that for each time step
- A three-dimensional lattice with internal symmetry group S4IN formed, which is responsible for the tetron order structure of elementary particles, as well as
- A three-dimensional space lattice with symmetry group S4sp, which induces a lattice structure on the Minkowski space, with lattice spacings of the order of the Planck scale.
The basic idea of this generalized Tetronmodells, therefore, is that both the space-time as well as the internal symmetry space possess a lattice structure, and that the two grids can be combined to a (6 1) unite - dimensional grid, with three of the (6 1) - dimensions are reserved for internal S4IN symmetry. As a fundamental dynamic field itself offers a (6 1) -dimensional spinor. The advantages of this model:
- As in all lattice theories with a fixed, finite lattice spacing there are no ultraviolet divergences and no need for renormalization.
- There are no no-go theorems such as the Weinberg -Witten theorem that forbid the unification of spatial and internal symmetries in continuous space.
- The (6 1 )-dimensional spinor is characterized in that it can be defined by means of the division algebra of octonions.
- Problems with the micro- causality, which usually occur with fermions on the lattice, with lattice spacings of the order of the Planck scale are not an issue since there causality is disturbed by quantum effects anyway.