Torsional Regularization of Self-Energy and Bare Mass of Electron

TL;DR

This paper introduces a torsion-based regularization method in quantum electrodynamics that removes divergences in self-energy calculations, providing finite bare masses for leptons that closely match observed values.

Contribution

It proposes a novel torsional regularization technique in QED, replacing divergent integrals with convergent sums using spacetime torsion effects.

Findings

Ultraviolet divergence in electron self-energy is eliminated.

Infrared divergence is absent in the torsional regularization.

Calculated bare lepton masses are approximately 85% of observed masses.

Abstract

In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum. In the Einstein--Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum. Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums. In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics. We show that torsion eliminates the ultraviolet divergence of the standard self-energy. We also show that the infrared divergence is absent. In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$, $90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively. These values constitute about $85\%$ of the observed, re-normalized masses.