Nonrelativistic inverse square potential, scale anomaly, and complex extension

DOI10.1016/j.aop.2009.10.002zbMath1193.81024arXiv0909.3477OpenAlexW3106352048WikidataQ61152494 ScholiaQ61152494MaRDI QIDQ848998

Sergej Moroz, Richard Schmidt

Publication date: 24 February 2010

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

Full work available at URL: https://arxiv.org/abs/0909.3477

zbMATH Keywords

limit cyclesfunctional renormalization groupconformal quantum mechanicsnonrelativistic conformal anomaly

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Exactly and quasi-solvable systems arising in quantum theory (81U15)

Related Items (19)

Quantitative unique continuation for the heat equations with inverse square potential ⋮ An efficient finite element method and error analysis for eigenvalue problem of Schrödinger equation with an inverse square potential on spherical domain ⋮ Point-particle effective field theory I: classical renormalization and the inverse-square potential ⋮ Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition ⋮ Viscosity and scale invariance in the unitary Fermi gas ⋮ Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions ⋮ Aharonov-Casher effect in the presence of spin-dependent potential ⋮ Scaling laws near the conformal window of many-flavor QCD ⋮ Stability of optimal control of heat equation with singular potential ⋮ A posteriori error estimation of hierarchical type for the Schrödinger operator with inverse square potential ⋮ The nonperturbative functional renormalization group and its applications ⋮ Renormalization group procedure for potential \(-g/r^{2}\) ⋮ The heat equation with strongly singular potentials ⋮ Breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition ⋮ Effective field theory of black hole echoes ⋮ New applications of the renormalization group method in physics: a brief introduction ⋮ Efimov physics from a renormalization group perspective ⋮ Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case ⋮ A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential

Cites Work

• Anti de Sitter space and holography
• Non-perturbative renormalization flow in quantum field theory and statistical physics
• On the limit cycle for the \(1/r^{2}\) potential in momentum space
• Aspects of the functional renormalisation group
• Black Holes and Superconformal Mechanics
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem
• Singular Potentials
• The three-body problem with short-range interactions
• Unnamed Item
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