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Despite the success of quantum field theories, the origin of the mass ofelementary particles persists. The renormalization program is an essential partof the calculation of the scattering amplitudes, where the infinities of thecalculated masses of the elementary particles are subtracted for theprogressive calculation of the higher-order perturbative terms. Themathematical structure of the mass term from quantum field theories expressedin the form of infinities suggests that there exists a finite dynamical mass inthe limit when the input mass parameter approaches zero. The Lagrangianrecovers symmetry at the same time as the input mass becomes zero, whereas theself-energy diagrams acquire a finite dynamical mass of the quantum fields inthe 4-dimensional space when the dimensional regularization method ofrenormalization is utilized. The complex forms of the QCD and QED interactionpotentials are obtained by replacing the fixed mass and coupling constants inthe Yukawa potential with the scale-dependent running coupling constant and thecorresponding dynamical mass. The derived QCD potential predicts quarkconfinement and deconfinement, and the QED potential derived by the same methodpredicts the sharply rising delta function potential near the contact distancebetween the electron and positron.

QCD QED Potentials, Quantum Field Theoretical Generalization of Yukawa Potential