Towards a matrix multi-level model of quark-gluon media

Abstract

The key feature of the model is an infinite sequence of canonical immersions of groups: U(2) into U(3), U(2) into U(4), and so on. Let us refer to these groups as to levels: U(2) – the 0^th level (that is, ours common), U(3) – the 1^st, U(4) – the 2^nd  and so on. Levels relate to (quarks’) generations whereas flavor and color are also defined purely mathematically. According to the model, quarks can be interpreted as ‘sank’ protons (during the beginning of the reaction process, proton (or rather the support U(2) of its wave function) is merely pushed into a deeper level. The model seems to be compatible with detection of point-like constituents within the proton in highly inelastic electron-proton scattering (and with elastic electron-quark scattering). To introduce gluons, we deal with proton-antiproton pairs (tensor product). At each level, a gluon can be interpreted as a colored 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 4^th generation).