Inertial motion of the quantum self-interacting electron

Abstract

Attempt to represent the self-interacting quantum electron as the cyclic motion has been discussed. This motion obeys the quantum inertia principle expressed by the parallel transported energy–momentum generator along a closed geodesic in the space of the unlocated quantum states CP(3) . The affine gauge potential in the complex projective state space (similar to the Higgs potential) seriously deforms the Jacobi fields in the vicinity of the “north pole”. It was assumed that the divergency of the Jacobi field may be compensated by the fields of the Poincaré generators representing EM-like “field shell” of the electron in the dynamical spacetime. Thereby, the spacetime looks as ultimately deprecated in the role of the “container of matter” and it appears as the accompanied to the quantum electron functional space (dynamical spacetime). Meanwhile, the dynamics of the self-interacting electron is essentially non-linear and deterministic.