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The Tetron Model was developed by Bodo Lampe in an attempt to reduce the 24 observed quark and lepton flavors and their interactions to a simple structure based on the permutation group S4, according to whose representations the quarks and leptons and also the vector bosons of the standard model can be ordered (see figure). A possible explanation of this ordering scheme is that the space of inner symmetries is not continuous, but has the form of a 3-dimensional lattice with tetrahedral symmetry (which is in fact isomorphic to the permutation group S4). The observed particles can be interpreted as excitations on this lattice and can be characterized by representations of this group.〔(B. Lampe, ''Development of the Tetron Model'', Found. of Phys., 39:215, 2009, ) 〕 ==Explanation in higher dimensions== A natural question to ask is, what the origin of the discrete inner S4 symmetry may be. To answer this question 〔(B. Lampe, ''Cosmological Implications of the Tetron Model of elementary Particles'', Cent. Eur. J. Phys. 8:771, ) 〕 one may consider a (fluctuating quantum) lattice in a 6+1 dimensional spacetime (e.g. with a S8 symmetry) and assume that by some unknown mechanism this symmetry is broken in such a way that for each timestep there is * a 3-dimensional inner lattice with symmetry group S4in responsible for the tetron ordering scheme of elementary particles and * a 3-dimensional spatial lattice with symmetry group S4sp inducing a discrete structure of Minkowski space, with lattice spacings of the order of the Planck scale. In other words, one assumes that inner symmetry space and Minkowski space both possess a discrete lattice structure and that both lattices can be united to a larger 6+1 dimensional lattice. Considering dynamical schemes on such a lattice is very appealing, for three reasons: * Ultraviolet divergences do not appear; correspondingly there is no need for renormalization. * No-go theorems like the Weinberg–Witten theorem which in the continuum forbid the unification of spatial and inner symmetries do not apply. * If one uses a 6+1 dimensional spinor as the fundamental dynamical field, such a spinor is closely related to the division algebra of octonions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tetron Model」の詳細全文を読む スポンサード リンク
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