On the limit cycle for the \(1/r^{2}\) potential in momentum space

DOI10.1016/j.aop.2005.04.017zbMath1091.81016arXivquant-ph/0503074OpenAlexW2024106644MaRDI QIDQ2368871

Brian Swingle, Hans-Werner Hammer

Publication date: 28 April 2006

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0503074

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (12)

Weyl consistency conditions in non-relativistic quantum field theory ⋮ Momentum approach to the 1/r2 potential as a toy model of the Wilsonian renormalization ⋮ Nonrelativistic inverse square potential, scale anomaly, and complex extension ⋮ Classical and quantum dynamics in an inverse square potential ⋮ On the inequivalence of renormalization and self-adjoint extensions for quantum singular interactions ⋮ Point-particle effective field theory I: classical renormalization and the inverse-square potential ⋮ Renormalization group analysis of boundary conditions in potential scattering ⋮ Renormalization of singular potentials and power counting ⋮ Renormalization group procedure for potential \(-g/r^{2}\) ⋮ Breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition ⋮ Efimov physics from a renormalization group perspective ⋮ Infrared realization of dS ₂ in AdS ₂

Cites Work

• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• Russian doll renormalization group and Kosterlitz-Thouless flows
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem
• Singular Potentials
• Strong-weak coupling duality in anisotropic current interactions
• A renormalized equation for the three-body system with short-range interactions

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