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 Poincare 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.