Perturbative hydrogenic Lamb shifts and radiative decay rates -- an so(4,2)-based algebraic approach

Quantum Physics [Submitted on 8 Apr 2026] Perturbative hydrogenic Lamb shifts and radiative decay rates -- an so(4,2)-based algebraic approach Gernot Alber It is shown that algebraic techniques based on the Lie algebra so(4,2) provide efficient tools for evaluating Lamb shifts and radiative decay rates for hydrogenic energy eigenstates as they systematically exploit the intrinsic symmetry of the hydrogenic Hamiltonian. As a main result in lowest order perturbation theory with respect to the fine-structure constant integral representations are derived for the complex-valued energy shifts of hydrogen-like ions from which Lamb shifts and radiative decay rates can be evaluated in a unified way, thus generalizing a recently discussed algebraic approach of Maclay. In order to exemplify the usefulness of this algebraic approach numerical results are presented for Lamb shifts and radiative decay rates which transcend the dipole approximation and contain the dipole approximation as a limiting case. Comments: 21 pages Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.06806 [quant-ph]   (or arXiv:2604.06806v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.06806 Focus to learn more Submission history From: Gernot Alber [view email] [v1] Wed, 8 Apr 2026 08:20:52 UTC (29 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)