The non-Abelian field current of the self-interacting quantum electron

Abstract

Internal degrees of freedoms of the quantum electron (spin and charge) introduced by Dirac lead to the non-Abelian field configuration of the electron in the complex projective Hilbert space $CP(3)$ of the unlocated quantum states (UQS). Such fields represented by the coefficient functions of the local dynamical variables (LDV's) corresponding $SU(4)$ generators of the Poincar\'e group. These generators describe the deformation of the UQS by the dynamical shifts, boosts and rotations. Interaction of this non-Abelian field with the electrodynamics-like gauge field (internal+external) will suppress the divergency of the Jacobi vector field in the vicinity of the "north pole" in $CP(3)$. Thereby, the stable "bundle" of the nearby geodesics comprises the lump-like quantum self-interacting electron.