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

Hirokazu Maruyama^*

• Independent Researcher, Kobe, Japan

We introduce fermion-boson transition functions as a statistical-mechanical approach to regulate ultraviolet divergences in quantum field theory. These functions describe how, above threshold energies, electrons acquire bosonic statistics while photons develop complementary fermionic components. Applied to quantum electrodynamics, this framework transforms divergent one-loop integrals into finite values without artificial cut-offs, while preserving BRST symmetry and Ward-Takahashi identities because the transition function is a gauge-invariant Lorentz scalar. Comparative analysis with dimensional regularization, Pauli-Villars, and hard cut-off methods confirms identical physical predictions, establishing our approach as a gauge-safe soft cut-off. The energy-momentum tensor associated with this formulation provides photons with longitudinal modes, suggesting a Higgs-free route to massive vector bosons. When extended to QCD, this framework offers unified perspectives on asymptotic freedom, colour confinement, and the gluon mass gap. Our statistical approach bridges high-energy physics and statistical mechanics, providing a conceptually transparent regulator applicable to analytical calculations, numerical simulations, and complex systems.