Related papers: Coarse graining and a new strategy for renormaliza…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We suggest that at any given order of Feynman diagram calculation all renormalization group (RG)-predictable terms should be resummed to all-orders. This ``complete'' RG-improvement (CORGI) serves to separate the perturbation series into…
Renormalisation group approaches are tailor made for resolving the scale-dependence of quantum and statistical systems, and hence their phase structure and critical physics. Usually this advantage comes at the price of having to truncate…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
We use renormalization group summed perturbation theory (RGSPT) to improve perturbation series in quantum chromodynamics in the determination of some of the standard model parameters.
We review some recent work on removing hidden confounding and causal regularization from a unified viewpoint. We describe how simple and user-friendly techniques improve stability, replicability and distributional robustness in…
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We re-examine some technical aspects of the subtractive renormalization, in particular, the mass…
Using a set of rephasing-invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We…
Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
While typical theories of atom-light interactions treat the atomic medium as being smooth, it is well-known that microscopic optical effects driven by atomic granularity, dipole-dipole interactions, and multiple scattering can lead to…
The Wilsonian exact renormalization group gives a natural framework in which ultraviolet and infrared divergences can be treated separately. In massless QED we introduce, as the only mass parameter, a renormalization scale $\L_R > 0$. We…