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

## TL;DR

This paper introduces a higher-dimensional Lagrangian framework for bi-cylindrical dynamical geometry to address the mass-hierarchy problem of charged leptons, linking geometric curvature with lepton masses.

## Contribution

It develops a novel higher-dimensional Lagrangian model incorporating a scalar gauge field within a bi-cylindrical geometry to explain lepton mass differences.

## Key findings

- Lepton masses can be derived from hyper-spherical surface curvatures.
- The model unifies general relativity with quantum field theory concepts.
- A scalar field acts as a gauge transformer in the 4D spacetime.

## Abstract

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.