Hydrogen energy levels from the anomalous energy-momentum QED trace

TL;DR

This paper calculates hydrogen energy levels using the QED energy-momentum tensor trace, linking trace diagrams to Lamb shift diagrams, and argues against including anomalous trace contributions separately in the Hamiltonian.

Contribution

It establishes a connection between trace diagrams and Lamb shift diagrams and clarifies the role of the trace anomaly in bound state QED.

Findings

Trace diagrams relate to Lamb shift diagrams

Anomalous trace contribution should not be separately included in the Hamiltonian

Provides insight into trace anomaly in bound state QED

Abstract

Energy levels of hydrogen are calculated as one-loop matrix elements of the QED energy-momentum tensor trace in the external field approximation. An explicit connection established between the one-loop trace diagrams and the standard Lamb shift one-loop diagrams. Our calculations provide an argument against inclusion of the anomalous trace contribution as a separate term in the decomposition of the QED quantum field Hamiltonian and serve as an illustration how the trace anomaly is realized in the bound state QED.