2006/11/17 by D. V. Shirkov, I. L. Solovtsov · 1 citation
Mathematics · Physics and Astronomy · #Causality (physics) #Gravitational singularity #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Mathematics #Observable #Particle physics #Particle physics theoretical and experimental studies #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Perturbative QCD #Physics #Power series #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Renormalization #Renormalization group #Series (stratigraphy) #Spurious relationship #Theoretical physics #hep-ph
paper · pdf · doi:10.1007/s11232-007-0010-7
published as Theor.Math.Phys.150:132-152,2007 · 26 pages, 9 figures, to be published in Theor. Math. Phys. (2007)
arxiv created 2006/11/17 · openalex publication_date 2007/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the Källen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.