Self-Gravitational Correction of the "Vacuum Polarization" Feynman Diagram Using Full Einstein Equation Propagation of the Intermediate Virtual Gravitons

TL;DR

This paper applies full Einstein equation propagation to correct the vacuum polarization Feynman diagram, rendering it finite and revealing significant deviations from standard QED behavior at Planck-scale energies.

Contribution

It introduces a self-consistent gravitational correction to quantum electrodynamics diagrams using Einstein equations, avoiding ultraviolet divergences and providing new insights at extreme energies.

Findings

Corrected diagram is finite and does not contribute to charge renormalization.

At Planck-scale energies, the correction causes the effective coupling to decrease toward zero.

The gravitational correction to the vacuum-to-vacuum amplitude vanishes.

Abstract

The self-gravitational correction of the ultraviolet-divergent second- order "vacuum polarization" radiative correction insertion Feynman diagram is carried out using full, self-consistent Einstein equation propagation of the intermediate virtual gravitons, which takes into account their important non-linear interactions with each other. (As a by-product, the subsequent perturbative treatment of these non-linearities is avoided, which eliminates the source of the ultraviolet divergences of the second- quantized gravity theory itself.) The corrected diagram is finite, makes no contribution to charge renormalization (as could be expected of a diagram involving but a single transient virtual pair), and its dynamical behaviour accords with the standard quantum electrodynamics result except at inaccessibly extreme (Planck-scale-related) values of the momentum transfer. There, the standard logarithmic rise with momentum transfer which this diagram contributes to the effective coupling strength falls away, as the diagram proceeds instead to decrease strongly toward zero. The same self-gravitational correction is made to the closely related quartically divergent second-order vacuum-to-vacuum amplitude correction Feynman diagram, and it is found that the result vanishes identically.