Classical renormalization of the point charge
Date of Award
Doctor of Philosophy (PhD)
Dentcho A. Genov
The objective of this dissertation is to renormalize the electron's self-energy, which is paradoxically infinite as a consequence of its point-charge description. We seek renormalization through the notion of a polarizable vacuum, a non-constant permittivity of free-space. A self-consistent model is possible when following three simple ansatzes: the permittivity of free-space converges to the constant value Eo for large (classical) distances, the electric potential of the electron converges to the Coulomb potential for large (classical) distances, and the electron's mass is purely electromagnetic. The three ansatzes provide a self-consistent model that abides by classical electromagnetism, provides short range corrections to classical theory, and renormalizes the electron's self-energy to follow the energy-mass relation.
Corrections to the Coulomb potential necessarily implies interaction energy corrections, which would contribute spectral splitting of an atom, such as positron. For this reason, we calculate the energy levels of the positronium atom with the renormalized electric potential and compare the first order contribution to the so-called Darwin term of relativistic quantum mechanics. The Darwin term can be interpreted as a shaking or jittering of the electron. We were able to simultaneously account for classical Coulombic interaction, pair annihilation (for the first time classically), and agreement with the Darwinian energy shifts.
Touchet, Brandon, "" (2016). Dissertation. 143.