Related papers: New Solutions for RG Equations in QCD
Based on the renormalization group summation method of McKeon ${\it et\; al.}$, it is shown that the renormalization group equation, while related to the radiatively mass scale $\mu$, would perform a summation over QCD perturbative terms.…
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization…
The renormalization group method is applied to the three-loop effective potential of the massive $\phi^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We work out the basic analysis of dynamics near QCD critical point (CP) by dynamic renormalization group (RG). In addition to the RG analysis by coarse graining, we construct the nonlinear Langevin equation as a basic equation for the…
Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type…
The analytization procedure which allows one to remove nonphysical singularities of the QCD running coupling constant $\bar\alpha_s(q^2)$ in the infrared region is applied to standard as well as to iterative solutions of the two-loop…
We analyze a formulation of QED based on the Wilson renormalization group. Although the ``effective Lagrangian'' used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's functions…
We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries.…
Renormalisation group (RG) methods provide one of the most important techniques for analysing the physics of many-body systems, both analytically and numerically. By iterating an RG map, which "course-grains" the description of a many-body…
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…
There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization…
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…
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a…
The basics of RG equations for generic partition functions are briefly reviewed, keeping in mind an application to the Polyakov-de Boer-Verlindes description of the holomorphic RG flow.
We investigate asymptotic behavior of solutions for nonlocal elliptic boundary value problems in plane angles and in ${\mathbb R}^2\backslash\{0\}$. Such problems arise as model ones when studying asymptotics of solutions for nonlocal…
In this PhD thesis, we analyze and generalize the renormalization group approach to the resummation of large logarithms in the perturbative expansion due to soft and collinear multiparton emissions. In particular, we present a…
Gauge theories are characterised by long range interactions. Neglecting these interactions at large times, and identifying the Lagrangian matter fields with the asymptotic physical fields, leads to the infra-red problem. In this paper we…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…