Computation of the leading order contributions to the Lamb shift for the H atom using spectral regularization

TL;DR

This paper presents a straightforward derivation of the Uehling potential function for the Lamb shift in hydrogen, avoiding complex renormalization techniques, and extends the method to compute the electron self-energy contribution.

Contribution

The paper introduces a conceptually simple, renormalization-free derivation of the Uehling potential and electron self-energy contributions for the Lamb shift, facilitating higher-order QFT calculations.

Findings

Derived the Uehling potential without renormalization.

Computed a matrix-valued potential for electron self-energy.

Method applicable to multi-loop QFT computations.

Abstract

The Uehling contribution to the Lamb shift can be computed exactly in terms of the Uehling potential function. However derivations of this function are complex involving avoiding divergences using intricate techniques from early quantum field theory (QFT) or else more modern approaches using charge and mass renormalization. In the present paper we derive the Uehling potential function in a fairly conceptually straightforward way not involving renormalization in which the vacuum polarization tensor is viewed as a Lorentz invariant 2-tensor valued measure on Minkowski space. Furthermore we compute a complex matrix valued potential function for the electron self-energy contribution to the Lamb shift. The resulting potential function is derived in a conceptually simple way not involving renormalization and can be used for higher order computations in QFT involving multiple loops.