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

Abstract

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.