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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, , and the negatively charged composite
fermion is considered as . 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
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