Proposal for statistical mechanics-based UV regularization using fermion-boson transition functions

Introduction We propose a statistical‐mechanics–based framework for UV regularization in QED/QFT by introducing energy‐dependent transition functions that interpolate fermionic and bosonic components. Methods We define logistic transition functions T(E) that continuously exchange degrees of freedom between γ_μ and ω_μ operators, and analyze gauge consistency via the Ward–Takahashi identities and BRST symmetry. Results The transition functions act as a smooth, gauge‐safe soft cutoff that exponentially suppresses UV contributions while preserving transversality. We illustrate how longitudinal components are cancelled in internal lines without affecting observables. Discussion This approach offers a physical (statistical) interpretation of regularization, unifies several phenomena across energy scales, and is compatible with Lorentz and gauge symmetries. Extensions to non‐Abelian theories and relations to mass generation mechanisms are outlined. Rationale These points correspond to Supplementary sections S9, S11–S19, S20, etc.