Mass Generation of Nuclear Force Mediators via Fermion–Boson Duality Theory and Extended Dirac Equation

Within the standard Yang–Mills framework alone, it is impossible to explain why the mediators of the nuclear force (pions, rho mesons, etc.) acquire non-zero masses. In this paper, we apply the Fermion–Boson Duality (FBD) theory and the extended Dirac equation based on a 256×256 matrix representation — established in prior peer-reviewed work — to the nucleon–meson system, and propose a mechanism in which mediator masses are dynamically generated through a statistical phase transition.

In the high-density environment inside nucleons, bosonic gluons undergo a statistical phase transition to fermionic gluons, generating an attractive contribution to the effective energy–momentum tensor. The spacetime metric is then distorted through the standard Einstein equation (left-hand side unchanged). This metric distortion is directly reflected in the anticommutation relation {Γ̂^μ(x), Γ̂^ν(x)} = 2g^μν(x)I₂₅₆ of the extended Dirac equation, thereby producing effective masses without any Higgs mechanism.

In the proposed framework, the finite range of the Yukawa-type potential — corresponding to the pion mass m_π ≈ 140 MeV — emerges as a natural consequence of the transition energy E_fb ~ Λ_QCD ≈ 200 MeV. The bosonic gamma matrices Ω automatically project onto the physical transverse degrees of freedom, eliminating the need for gauge fixing and Faddeev–Popov ghosts.

Key results:

1. Mass generation mechanism: Mediator masses are dynamically generated through the statistical phase transition (g_B → g_F) inside nucleons, without introducing Proca-type mass terms or the Higgs mechanism.
2. Natural derivation of the Yukawa potential: The pion mass m_π ≈ 140 MeV emerges naturally from the transition energy E_fb ~ Λ_QCD.
3. Unified description: BCS superconductivity, the emergence of gravity [doi:10.5281/zenodo.18794827], and the nuclear force are all described within the same FBD statistical-mechanical framework.
4. Ghost-free formulation: No gauge fixing or Faddeev–Popov ghosts are required.

The approach exactly recovers standard QCD and general relativity in the low-energy limit.

This paper is a theoretical proposal and is being prepared for journal submission.