Self-Interacting Electron as a Nonlinear Dynamical System

Abstract

We have proposed a simple one-dimensional model of internal particle dynamics. The model is based on the assumption that self-interaction can be represented by a nonlinear feedback and described by a quadratic recurrent map. Charge plays the role of a generalized dynamical variable and a feedback coupling parameter. The model suggests that charge and action quantization stem from the system's dissipative quality and from a hierarchy of supercycle orbits located between period-doubling bifurcations on the Feigenbaum tree. Among the numerical results, we have discovered a link between the quantum of action and the elementary charge. We also found that the fine structure constant can with a good accuracy be expressed exclusively through mathematical constants, including the Feigenbaum delta. We have introduced dimensionless numbers that describe the relative role of the internal particle dynamics when both internal and external dynamics are taken into consideration. We have found these numbers to be close to the electron, proton, and neutron g-factors known from the experiment.