Hydrogen energy levels from the anomalous energy-momentum QED trace

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.

35 pages, 10 figures;v2:Minor amendments, discussion of the results expanded, additional references and acknowledgments added, results unchanged; v3: Abstract amended; v4: published version