Pauli Exclusion Principle and Nonlinear Dirac Equation

Abstract

The nonlinear Dirac equation is a magical equation that hides manymysteries of nature, so it is worth systematic study. In this paper,we give a detailed analysis for the effects of various covariantpotential terms on the energy eigenstates and the representationspace as well as the solvability of the spinor equation, and weobtain the specific potential energy terms that lead to the standingwave solutions. By simplifying the spinor equation, we find that thenonlinear pseudo scalar potential causes the oscillation anddivergence of the radial wave function, so the nonlinear weakinteraction between spinors may be the dynamical reason of Pauliexclusion principle. The nonlinear potentials of a spinor has somewonderful properties, such as the confinement of negative energystate, the generation of negative pressure and celestial magneticfield, etc. We also present a calculating method for solving theDirac equation with complicated potentials, which may be a usefultool for further uncovering the mysteries of elementary particles.