Hypothesis of path integral duality: Applications to QED

TL;DR

This paper explores a modified quantum electrodynamics (QED) propagator based on path integral duality, which introduces a fundamental length scale to regulate divergences and analyze radiative corrections, with implications for primordial magnetic fields.

Contribution

It applies a path integral duality-based propagator to QED, demonstrating divergence removal and finite renormalization factors, while examining gauge invariance breaking effects.

Findings

Modified propagator acts as a Planck-scale regulator.

Renormalization factors become finite with the new propagator.

Gauge invariance is broken at an extremely small level.

Abstract

We use the modified propagator for quantum field based on a ``principle of path integral duality" proposed earlier in a paper by Padmanabhan to investigate several results in QED. This procedure modifies the Feynman propagator by the introduction of a fundamental length scale. We use this modified propagator for the Dirac particles to evaluate the first order radiative corrections in QED. We find that the extra factor of the modified propagator acts like a regulator at the Planck scales thereby removing the divergences that otherwise appear in the conventional radiative correction calculations of QED. We find that:(i) all the three renormalisation factors $Z_1$, $Z_2$, and $Z_3$ pick up finite corrections and (ii) the modified propagator breaks the gauge invariance at a very small level of ${\mathcal{O}}(10^{-45})$. The implications of this result to generation of the primordial seed magnetic fields are discussed.