Zimmermann's Forest Formula, Infrared Divergences and the QCD Beta Function

We review Zimmermann's forest formula, which solves Bogoliubov's recursive $R$-operation for the subtraction of ultraviolet divergences in perturbative Quantum Field Theory. We further discuss a generalisation of the $R$-operation which subtracts besides ultraviolet also Euclidean infrared divergences. This generalisation, which goes under the name of the $R^*$-operation, can be used efficiently to compute renormalisation constants. We will discuss several results obtained by this method with focus on the QCD beta function at five loops as well as the application to hadronic Higgs boson decay rates at N${}^4$LO. This article summarizes a talk given at the Wolfhart Zimmermann Memorial Symposium.Comment: 17 pages, 5 figures; based on a talk given at the Wolfhart Zimmermann Memorial Symposium on the 22nd of May 2017 in Munic

Systematic Differential Renormalization to All Orders

We present a systematic implementation of differential renormalization to all orders in perturbation theory. The method is applied to individual Feynamn graphs written in coordinate space. After isolating every singularity. which appears in a bare diagram, we define a subtraction procedure which consists in replacing the core of the singularity by its renormalized form givenby a differential formula. The organizationof subtractions in subgraphs relies in Bogoliubov's formula, fulfilling the requirements of locality, unitarity and Lorentz invariance. Our method bypasses the use of an intermediate regularization andautomatically delivers renormalized amplitudes which obey renormalization group equations.Comment: TEX, 20 pages, UB-ECM-PF 93/4, 1 figureavailable upon reques

No radiative generation of Chern-Simons-like term in Lorentz-violating QED: dealing with IR divergences

The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction -- the axial coupling of fermions with a constant vector field b_\m -- is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.Comment: In honor of Prof. Manfred Schweda (1939-2017). Work presented at the XXXVIII National Meeting on Particle Physics and Fields, September 18-22, 2017 - Passa Quatro - Minas Gerais - Brazil. Reference [46] correcte

Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene

The two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study using the BPHZ prescription. Non-standard Ward identities imply that divergent subgraphs (related to Fermi velocity renormalization) contribute to the renormalized optical conductivity. Proceeding either via density-density or via current-current correlation functions, a single well-defined value is obtained: $\mathcal{C}= (19-6\pi)/12) = 0.01$ in agreement with the result first obtained by Mishchenko and which is compatible with experimental uncertainties.Comment: LaTeX file with feynMF package. (v2) Footnotes and references added to answer referee's questions and comments. No change in results. 23 pages (JHEP format), 4 figures (v1) 12 pages, 4 figure