Renormalization and Non-perturbative Dynamics in Conformal Quantum Mechanics

Quantum Physics [Submitted on 16 Apr 2026] Renormalization and Non-perturbative Dynamics in Conformal Quantum Mechanics Jacob Hafjall, Thomas A. Ryttov We study conformal quantum mechanics by first considering the perturbative S-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the two couplings. We then focus on the inverse square potential in one spatial dimension and compute the beta function to arbitrarily perturbative and non-perturbative orders. This we do in both the bound state sector and scattering sector. We provide explicit, exact and infinite series results of the first few non-perturbative orders. Comments: 40 pages, 1 figure Subjects: Quantum Physics (quant-ph); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2604.15412 [quant-ph]   (or arXiv:2604.15412v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.15412 Focus to learn more Submission history From: Thomas A. Ryttov [view email] [v1] Thu, 16 Apr 2026 16:50:57 UTC (53 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: hep-ph hep-th 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?)