Abstract: A fundamental role of linear-fractional transformations in different spaces of matrices is well-known. The current research mainly deals with one such space: D. As a space-time, D can be viewed as a Lie group with causal structure determined by an invariant Lorentzian form on the Lie algebra u(2). Recently, the author suggested a matrix multi-level model of quarks and gluons. As a basis for this model, the Segal's compact cosmos D has been employed as well as the sequence of canonical (that is, corresponding to principal minors of appropriate matrices) group embeddings: U(2) into U(3), U(2) into U(4), etc. These groups were called the levels (of matter): U(2) - the 0th (that is, our mundane), U(3) - the 1st, U(4) - the 2nd, etc. Such a convention matches the standard quarks' generations' list. Seemingly, the multi-level model is the only known construct where such notions as flavour and colour are defined mathematically. According to the model, a quark can be interpreted as a 'sank' proton (during the beginning of the reaction process, proton 'is pushed' into a 'deeper' level). At each level, a gluon can be interpreted as a colored and flavored photon. Not each and every feature of the model coincides with the corresponding standard assumption about quarks and gluons. In particular, the total number of colors is level-dependent. The model predicts THREE new quarks of the 4th generation (whereas currently there is a search for TWO). © 2019 Published under licence by IOP Publishing Ltd.

Cite: Levichev A.V.
One possible application of the Chronometric Theory of I.E. Segal: A toy model of quarks and gluons
Journal of Physics: Conference Series. 2019. V.1194. N1. 012071 . DOI: 10.1088/1742-6596/1194/1/012071 Scopus OpenAlex

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Scopus:	2-s2.0-85065562030
OpenAlex:	W2941114722

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