Closed String Approximation in the Skyrme–Faddeev Chiral Model: Charged Lepton Sector

As a possible realization of Einstein’s idea of representing particles as solitons, i.e., clots of some nonlinear universal field, the Brioschi 16-spinors are introduced, these complex projective coordinates in the 8-geometry being well suited for the role of that fundamental “unitary field.” Within the scope of the 16-spinor realization of the Skyrme–Faddeev chiral model (SFCM), it is suggested to describe the family of charged leptons, including the electron, the muon and the taon, as topological solitons endowed with the Hopf topological invariant $Q_{\textrm{H}}$, which can be interpreted, following Faddeev, as the lepton number $\mathbb{L}$. For constructing axially symmetric topological soliton configurations, group theoretical analysis based on the Coleman–Palais principle of symmetric criticality is applied. Taking into account that according to Faddeev’s suggestion, these soliton configurations should have a closed string structure, the corresponding approximation method is used, its effectiveness being proven. Finally, spins and masses of the soliton configurations are found.