# Angular momentum of the electron: One-loop studies

## TL;DR

This paper investigates one-loop radiative corrections to the electron's angular momentum in quantum electrodynamics, emphasizing the importance of imaginary time evolution and regularization techniques for accurate results.

## Contribution

It introduces a formalism combining bare perturbation theory with imaginary time evolution and develops a modified Pauli-Villars regularization for angular momentum calculations.

## Key findings

- Proper imaginary time implementation is crucial for correct total angular momentum.
- A modified Pauli-Villars regularization ensures consistent angular momentum results.
- The formalism accurately separates spin and orbital angular momentum components.

## Abstract

We combine bare perturbation theory with the imaginary time evolution technique to study one-loop radiative corrections to various components of angular momentum of the electron. Our investigations are based on the canonical decomposition of angular momentum, where spin and orbital components, associated with fermionic and electromagnetic degrees of freedom, are individually approached. We use for this purpose quantum electrodynamics in the general covariant gauge and develop a formalism, based on the repeated use of the Sochocki-Plemelj formula, for proper enforcement of the imaginary time limit. It is then shown that careful implementation of imaginary time evolutions is crucial for getting a correct result for total angular momentum of the electron in the bare perturbative expansion. We also analyze applicability of the Pauli-Villars regularization to our problem, developing a variant of this technique based on modifications of studied observables by subtraction of their ghost operator counterparts. It is then shown that such an approach leads to the consistent regularization of all angular momenta that we compute.