Proposal for Statistical Mechanics-Based UV Regularization Using Fermion-Boson Transition Functions

This paper introduces a novel statistical mechanics-based approach to ultraviolet regularization in quantum field theory using fermion-boson transition functions. The proposed framework describes how electrons acquire bosonic statistics and photons develop fermionic components above threshold energies, transforming divergent one-loop integrals into finite values without artificial cut-offs. The approach preserves BRST symmetry and Ward-Takahashi identities while providing a gauge-safe soft cut-off mechanism. When applied to QED, this formulation enables photons to acquire longitudinal modes, suggesting a Higgs-free route to massive vector bosons. Extended to QCD, the framework offers unified perspectives on asymptotic freedom, color confinement, and the gluon mass gap. This approach bridges high-energy physics and statistical mechanics, providing a conceptually transparent regularization method applicable to analytical calculations, numerical simulations, and complex systems. --- Version 2 update ---This version replaces the original preprint with the peer-reviewed accepted manuscript.Published in: Frontiers in Physics, vol. 13, 1618853 (2025).DOI: https://doi.org/10.3389/fphy.2025.1618853 The uploaded files are the author's LaTeX version (standard article class) of the published article and its supplementary material. The content is identical to the peer-reviewed published version. Numerical codes (Mathematica) supporting this paper are available at:- FBD transition function UV regularization code: https://doi.org/10.5281/zenodo.15825707- 256×256 extended Dirac equation scattering calculations: https://doi.org/10.5281/zenodo.18708276