2015/05/12 by Alessandro Codello, Roberto Percacci, Lesław Rachwał +2 · 43 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Effective action #Functional renormalization group #Gauge theory #Graviton #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field theory #Scattering amplitude #gr-qc #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1140/epjc/s10052-016-4063-3
published in The European Physical Journal C 76(4) (Springer Science+Business Media) · 40 pages
arxiv created 2015/05/12 · openalex publication_date 2016/04/01 · arxiv updated 2016/05/25 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k . The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k=Λ down to k=0 . We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang–Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.