Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I

TLDR

The nucleon mass is proposed to arise mainly as a self‑energy of a primary fermion field, analogous to the energy gap in superconductivity. The study examines paradoxical aspects of the theory related to the γ5 transformation. The authors formulate the model using a generalized Hartree‑Fock approximation that treats nucleons as quasiparticle excitations and a simplified nonlinear four‑fermion interaction with a γ5 gauge symmetry. The symmetry yields pseudoscalar zero‑mass nucleon‑antinucleon bound states that can be viewed as an idealized pion, and predicts massive bound states with nucleon number zero and two, with two parameters linked to the observed nucleon mass and pion‑nucleon coupling.

Abstract

It is suggested that the nucleon mass arises largely as a self-energy of some primary fermion field through the same mechanism as the appearance of energy gap in the theory of superconductivity. The idea can be put into a mathematical formulation utilizing a generalized Hartree-Fock approximation which regards real nucleons as quasi-particle excitations. We consider a simplified model of nonlinear four-fermion interaction which allows a ${\ensuremath{\gamma}}_{5}$-gauge group. An interesting consequence of the symmetry is that there arise automatically pseudoscalar zero-mass bound states of nucleon-antinucleon pair which may be regarded as an idealized pion. In addition, massive bound states of nucleon number zero and two are predicted in a simple approximation.The theory contains two parameters which can be explicitly related to observed nucleon mass and the pion-nucleon coupling constant. Some paradoxical aspects of the theory in connection with the ${\ensuremath{\gamma}}_{5}$ transformation are discussed in detail.