The effect of nucleus size on the electron energy levels: via Seiberg-Witten map

TL;DR

This paper compares two approaches to non-commutative geometry effects on electron energy levels, revealing their differences and how they influence physical quantities like dipole moments and vertex corrections.

Contribution

It demonstrates the non-equivalence of Bob's shift method and Seiberg-Witten map in analyzing non-commutative effects on electron energy levels.

Findings

The two methods produce different corrections to energy levels.

Dipole moments are affected differently by each approach.

Vertex corrections vary depending on the mapping used.

Abstract

We compare the effects of the entering non - commutative geometry in physics, which have studied by Bob's shift method and Seiberg-Witten map. Due to the corrections of the electron energy levels, we demonstrate that two approaches are not equivalent. We show that the electric and magnetic dipole moments, as well as one loop vertex correction, change due to the mapping selection. Furthermore, we provide a way to communicate the results of the two methods.