Related papers: Renormalization Scheme Dependence and Renormalizat…
We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the…
When one uses the Coleman-Weinberg renormalization condition, the effective potential $V$ in the massless $\phi_4^4$ theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the…
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 present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
A systematic method is proposed for analyzing the renormalization scheme uncertainties in the next-next-to-leading order QCD predicitions, based on a condition which eliminates schemes that give rise to large cancellations in the expression…
We construct simple analytical solutions of renormalization group equations for the running coupling and for the Green functions in QCD in the asymptotic regime. These solutions have an explicit form and subsequently sum up the leading,…
Renormalization factors relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. They have to be computed very precisely which requires a careful treatment of…
The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group…
Using as an example the Einstein gravity with the cosmological constant, we discuss the calculation of renormalization group functions off shell. We found, that gauge dependent terms should be absorbed by the nonlinear renormalization of…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in…
In the absence of a tree-level scalar-field mass, renormalization-group (RG) methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series for the effective-potential functions utilized in…
We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is…
Quantum field theories containing scalar fields with equal quantum numbers allow for a mixed kinetic term in the Lagrangian. It has been argued that this mixing must be taken into consideration when performing renormalization group (RG)…
The QCD coupling, $\alpha_s$, is not a physical observable since it depends on conventions related to the renormalization procedure. Here we discuss a redefinition of the coupling where changes of scheme are parametrised by a single…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…
Any effective field theory relies on power counting rules that allow one to perform a systematic expansion of calculated quantities in terms of some soft scales. However, a naive power counting can be violated due to the presence of various…
Previously proposed procedure for improving the effective potential by using renormalization group equation (RGE) is generalized so as to be applicable to any system containing several different mass scales. If one knows L-loop effective…
We discuss the gauge dependence of fermion mass definition and physical result under the conventional on-shell mass renormalization scheme and the recently proposed pole mass renormalization scheme in standard model. By the two-loop…
The application of renormalization group techniques to bound states in non-relativistic QED and QCD is discussed. For QED bound states like Hydrogen and positronium, the renormalization group allows large logarithms of the velocity, ln v…