Four-dimensional symmetry from a broad viewpoint X.—Finite self-masses and the proton-neutron mass difference

Abstract

We show that the self-mass is finite in this theory with the universal probability for field oscillators. The «bare mass» of the photon in finite QED is related to the fundamental massMf by the relationmγ2≈αMf2/2π. The electromagneticU1 gauge symmetry with the massless photon is the result of the interaction and finite renormalization. Finite «quantum elecweakdynamics» with quarks can lead to the correct sign and the right order of magnitude of the mass differences for nucleons and other hadron isomultiplets. Usual quantum field theories based on special relativity cannot explain these observed mass differences. Furthermore, the present elecweakdynamics suggests that there is a large violation of the isospin invariance due to a mass difference between up and down quarks. It also indicates that the observed lepton masses are smaller than the corresponding bare masses. All these results of self-masses are essentially the same no matter whether one uses an exponential function, exp [−IG], or a rational function, (I2G2+1)−2, for the universal probability distribution of field oscillators.