Abstract
This paper continues the author’s work [1], where a new framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation was discovered. Here, the nonlinear Dirac equation is solved and the localized configurations are found analytically. Of the two possible types of the potentially stationary localized configurations of the Dirac field, only one is stable with respect to the action of an external field and it corresponds to a positive charge. A connection with the global charge asymmetry of matter in the Universe and with the recently observed excess of the cosmic positrons is discussed.
Highlights
This paper continues the author’s study of the long-standing question of how the physical Dirac field of a real matter becomes a finite-sized particle, and it is approached here as a practical problem
The problem is posed and solved in a new framework of the matter-induced affine geometry [1], which deduces the geometric relations in the space-time continuum from the dynamic properties of the Dirac field
The intuitive argument of a possible auto-localization of the Dirac field followed from an observation [1] that the local time flows slower at higher invariant density, and from the wave nature of the Dirac equation
Summary
This paper continues the author’s study of the long-standing question of how the physical Dirac field of a real matter becomes a finite-sized particle, and it is approached here as a practical problem. It is observed that if at a point in spacetime continuum (the principal differentiable manifold ) a physical Dirac field is defined, the latter determines the tetrad of Dirac currents. The inevitable localization of the Dirac field into particles observed in real world, but not explained by any theory so far, is confirmed by the analytic solutions of the nonlinear Dirac equation in one-body approximation. This representation is well suited for finding the analytic solution. The conceptual questions of the charge-asymmetric real world are briefly discussed in the Summary
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