Frobenius 3-Folds via Singular Flat 3-Webs

We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the Chern connection form is holomorphic, 3) the curvature form vanishes identically

Muon as a composite fermion from the three charged electron-like leptons in the bound state in the continuum

For many-particle systems the mass of the bound states in the continuum (BIC) is greater than the total mass of the initial particles. BICs which are stable and not-decaying, have been found and studied in detail in various fields of physics. But, as far as we know, in particle physics such states have not yet been analyzed. The idea of this work is to apply the BIC phenomenon to some elementary particles and, in particular, to the description of muons. This study focuses on a composite fermion formed by the three charged electron-like leptons in BIC, with the mass of 207 electron masses. The structure of the positive charged composite fermion is formed by the two positron and the electron, $(e^{+}e^{+}e^{-})_{BIC}$, and the negatively charged composite fermion is considered as $(e^{-}e^{-}e^{+})_{BIC}$. In this theory the free electron and free positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves. The integral equation for the wave function of the composite fermion is derived by using the Bethe and Salpeter equation with account for the lowest order of the pair interaction for the three particles. An approximate solution of this equation gave results for the massive fermion wave function that predicted the particle radius equal to 16 fm. The representation of the muon as the composite fermion formed by the three charged electron-like leptons in BIC, is analyzed. Only in the case of considering the electron and positron as ordinary, different particles, the possible decay channels of this heavy composite fermion do not contradict those for the muons.Comment: 16 pages, 5 figure