On the Origin of Charge-Asymmetric Matter. III. Properties of Autolocalized Dirac Waveforms

This paper continues the author’s work [1] [2], where a novel framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation was discovered. The previous analysis of solitary waveforms’ properties [2] is extended to the four-component Dirac field. It is found that the internal spherical symmetry of the Dirac waveforms is broken to the axial one. The nonlinear Dirac equation is solved and the localized configurations are found analytically. A strict proof that the proper time slowdown is the major mechanism of autolocalization is presented. The previous qualitative conjecture regarding stability or instability of the two types of the waveforms and the origin of cosmological charge asymmetry is supported by detailed analysis. A solution of the problem of mapping between the matter-induced geometry of autolocalized waveforms and the geometry of an ambient Minkowski space is proposed. These results resolve the longstanding puzzle of how the physical Dirac field of real matter becomes a finite-sized particle.

On the Origin of Charge-Asymmetric Matter. I. Geometry of the Dirac Field

This work presents new round of the author’s pursuit for consistent description of the finite sized objects in classical and quantum field theory. Current paper lays out an adequate mathematical background for this quest. A novel framework of the matter-induced physical affine geometry is developed. Within this framework, (1) an intrinsic nonlinearity of the Dirac equation becomes self-explanatory;(2) the spherical symmetry of an isolated localized object is of dynamic origin;(3) the auto-localization is a trivial consequence of nonlinearity and wave nature of the Dirac field;(4) localized objects are split into two major categories that are clearly associated with the positive and negative charges;(5) of these, only the former can be stable as isolated objects, which explains the global charge asymmetry of the matter observed in Nature. In the second paper, the nonlinear Dirac equation is written down explicitly. It is solved in one-body approximation (in absence of external fields). Its two analytic solutions unequivocally are positive (stable) and negative (unstable) isolated charges. From the author’s current perspective, the so for obtained results must be developed further and applied to various practical and fundamental problems in particle and nuclear physics, and also in cosmology.

On the Origin of Charge-Asymmetric Matter. II. Localized Dirac Waveforms

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.