A higher-dimensional Lagrangian representation of bi-cylindrical dynamical geometry for the mass-hierarchy problem of charged leptons

According to our microscopic cosmological model, masses of charged leptons can be calculated by curvatures of hyper-spherical surfaces embedded in a 3D time-like subspace. In this study, a higher-dimensional Lagrangian representation is applied to the bi-cylindrical dynamical geometry. A four-component scalar field is assumed to serve as the gauge transformers in the linearly factorized 4D space-time for inducing lepton mass. The consistency of the general relativity approach with quantum field theories is discussed.