Related papers: Renormalization: an advanced overview
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Wetterich's equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quantum scale invariance. Motivated by recent works on asymptotically safe scalar-tensor…
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…
In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
In this talk I will discuss a number of approaches designed to deal with the problem of setting up a fully non-perturbative renormalization procedure in lattice QCD. Methods based on Ward-Takahashi identities on hadronic states, on imposing…
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is considered.
We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a…
The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and…
I review the strategies which have been developped in recent years to solve the non-perturbative renormalization problem in lattice field theories. Although the techniques are general, the focus will be on applications to lattice QCD. I…
Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based…
We suggest a renewed view on non-renormalizable interactions treated perturbatively within a kinematically dependent renormalization procedure. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT…