Physical Vacuum – Part I Spectral vacuum mechanism (SVM) Lepton Mass Hierarchies

Abstract

We propose a structural vacuum model (SVM) in which the observed hierarchy of charged lepton masses arises as a spectral property of localized fluctuation modes around a vacuum configuration. The model is formulated in terms of a coupled second-variation (Hessian) operator acting on three fluctuation channels in a one-dimensional domain. Particle masses are identified with the square roots of positive eigenvalues of this operator, up to a single absolute calibration fixed by the electron mass.

The main goal of this work is not to postulate a microscopic Lagrangian, but to demonstrate that a minimal and internally consistent vacuum structure can simultaneously satisfy stability, localization, and strong spectral separation, reproducing the electron–muon–tau hierarchy without Yukawa couplings or multi-parameter fitting. The paper focuses on structural necessity: which features of the Hessian operator are unavoidable if such hierarchies are to exist at all.

Keywords: structural vacuum model, lepton mass hierarchy, spectral mechanism, vacuum fluctuations, hessian operator, localized modes, mass generation, absence of yukawa couplings, multi-scale vacuum structure, spectral stability, minimality principle, robustness analysis, electron muon tau hierarchy, variational vacuum approach, eigenvalue spectrum