Tetron model

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Assignment of quarks and leptons to permutation states

The tetron model is an attempt to the 24 observed quark - and Lepton - Flavors due and their interactions in a more simple structure. It is based on the structure of the permutation group  S 4 , according to whose representations the quarks and leptons (and also the vector boson states) of the standard model can be arranged (see graphic).

A possible explanation of this ordering scheme was suggested by Bodo Lampe . It consists in the assumption that the area of internal symmetry is not continuous, but a three-dimensional lattice having tetrahedral symmetry (which is isomorphic to S 4 - symmetry group is). The observed particles can be interpreted as excitations on this lattice, which are characterized by the representations of the lattice symmetry group.

Explanation in higher dimensions

The question then automatically arises as to the origin of the discrete inner S 4 symmetry. To answer this question, a (fluctuating quantum) lattice in a (6 + 1) -dimensional space-time was considered in Ref. (E.g. with S 8 as a symmetry group), the symmetry of which is broken so that for each time step

  • a three-dimensional inner lattice with symmetry group S 4 in is created, which is responsible for the tetron order structure of the elementary particles, as well as
  • a three-dimensional space lattice with a symmetry group S 4 sp , which induces a lattice structure on the Minkowski space , with lattice spacings of the order of magnitude of the Planck scale .

The basic idea of ​​this generalized Tetron model is that space-time as well as the inner symmetry space have a lattice structure and that the two lattices can be combined to form a (6 + 1) -dimensional lattice, with three of the (6 + 1) -dimensions are reserved for the inner S 4 in symmetry. A (6 + 1) -dimensional spinor can be used as a fundamental dynamic field . The advantages of this model:

  • As in all lattice theories with a fixed, finite lattice spacing, there are no UV divergences and no need for renormalization .
  • There are also no no-go theorems like the Weinberg-Witten theorem that prohibit the unification of spatial and internal symmetries in continuous space.
  • The (6 + 1) -dimensional spinor is distinguished in that it, with the aid of the division algebra of octonions can be defined.
  • Problems with the micro-causality , which usually occur with fermions on the lattice, are not an issue with lattice spacings of the order of magnitude of the Planck scale, since there the causality is disturbed by quantum effects anyway.

Individual evidence

  1. ^ B. Lampe, Development of the Tetron Model , Found. of Phys., 39: 215, 2009, doi : 10.1007 / s10701-009-9278-9 .
  2. ^ B. Lampe, Cosmological Implications of the Tetron Model of elementary Particles , Cent. Eur. J. Phys. 8: 771, doi : 10.2478 / s11534-010-0002-3 .