Related papers: Systematic Differential Renormalization to All Ord…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
A perturbation scheme is discussed for the computation of the normalization constant of the large order behavior arising from an ultraviolet renormalon. In this scheme the normalization constant is expressed in a convergent series that can…
We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…
We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…
Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $\epsilon$-poles, allowing to define counter-terms with useful recursive…
An algorithm for the reduction of massive Feynman integrals with any number of loops and external momenta to a minimal set of basic integrals is proposed. The method is based on the new algorithm for evaluating tensor integrals,…
Recently, we have developed a formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. This corresponds to an all-order resummation of certain terms (the so-called renormalon…
We apply the diagrammatic renormalization method to the NLO analysis of the $2^{++}$ tensor di-gluonium channel within the QCD sum-rules approach. Diagrammatic renormalization eliminates non-local divergences directly, avoiding the…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
One of the main sources of theoretical uncertainty in the extraction of the strong coupling from hadronic tau decays stems from the renormalization-group improvement of the series. Perturbative series in QCD are divergent but are (most…
In this article, we define a doubling procedure for the bialgebra of specified Feynman graphs introduced in a previous paper \cite {DMB}. This is the vector space generated by the pairs $(\bar \Gamma, \bar \gamma)$ where $\bar \Gamma$ is a…
The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly…
Using the renormalization group techniques it was previously shown that the perturbative effective potential in the $\mathcal{O}(N)$ symmetric $\phi^4$ theory, massless scalar electrodynamics as well as in the conformal limit of the…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
We investigate the use of renormalisation group methods to solve partial differential equations (PDEs) numerically. Our approach focuses on coarse-graining the underlying continuum process as opposed to the conventional numerical analysis…
This paper is the fifth in a series devoted to the development of a rigorous renormalisation group method applicable to lattice field theories containing boson and/or fermion fields, and comprises the core of the method. In the…
We present a subtraction scheme for ultraviolet (UV) divergent, infrared (IR) safe scalar Feynman integrals in dimensional regularization with any number of scales. This is done by the introduction of $u$-variables, which are a suitable…