Wavelet regularization of Euclidean QED

TL;DR

This paper introduces a wavelet-based regularization method for Euclidean quantum electrodynamics, analyzing scale-dependent functions and calculating vacuum polarization and effective coupling in one-loop approximation.

Contribution

It presents a novel regularization approach using wavelet transforms in Euclidean space, incorporating scale dependence into QED calculations.

Findings

Calculated vacuum polarization in one-loop approximation.

Determined scale dependence of the effective coupling constant.

Demonstrated the applicability of wavelet regularization in Euclidean QED.

Abstract

The regularization of quantum electrodynamics in the space of functions $\psi_a(x)$, which depend on both the position $x$ and the scale $a$, is presented. The scale-dependent functions are defined in terms of the continuous wavelet transform in $\mathbb{R}^4$ Euclidean space, with the derivatives of Gaussian served as basic wavelets. The vacuum polarization and the dependence of the effective coupling constant on the scale parameters are calculated in one-loop approximation in the limit $p^2 \gg 4m^2$.