Mathematica Notebooks for FBD–QCD: Asymptotic Freedom, Confinement, and UV Regularization

This Zenodo record provides Mathematica notebooks implementing the Fermion-Boson Duality (FBD) approach to quantum chromodynamics (QCD). The codes generate numerical results and figures demonstrating the FBD-QCD effective potential, natural UV regularization of loop integrals via energy-dependent transition functions, and verification of the algebraic properties of the bosonic gamma matrices ω_μ.

The archive contains the following notebooks:

1. FBD_QCD_Effective_Potential_and_Loop_Regularization.nb
     Part A: Unified description of asymptotic freedom and confinement
      Defines gluon and quark transition functions T_g(E) and T_q(E)
      Implements F-type (Cornell) and B-type (Coulomb) potentials
      Computes energy-dependent effective potential V_eff(E,r)
      Generates figures for transition functions, potentials, forces, and running couplings
     Part B: UV regularization of 1-loop self-energy (toy model)
      Evaluates gluon loop, quark loop, ghost loop, quark self-energy, and 3-gluon vertex corrections
      Compares standard QCD (divergent) with FBD-QCD (convergent)
      Demonstrates suppression factors of ~10^8 for loop integrals
      Verifies convergence as k_max → ∞

2. omega_matrix_properties.nb
    Defines standard Dirac gamma matrices γ^μ in 4×4 matrix form
    Constructs bosonic gamma matrices ω_μ = (γ_0+γ_3)/2, γ_1, γ_2, (γ_3+γ_0)/2
    Verifies anticommutation relations {ω_μ, ω_ν}
    Confirms the invariant (ω_μ A^μ)² = −A_1² − A_2², showing only transverse degrees of freedom propagate