Related papers: A Systematic All-Orders Method to Eliminate Renorm…
The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost)…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
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…
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…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
The explorations of models beyond the Standard Model (BSM) naturally involve scans over the unknown BSM parameters. On the other hand, high precision predictions require calculations at the loop-level and thus a renormalization of (some of)…
As one of the key components of perturbative QCD theory, it is helpful to find a systematic and reliable way to set the renormalization scale for a high-energy process. The conventional treatment is to take a typical momentum as the…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…
A renormalization scheme is suggested where QCD input parameters - quark mass and coupling constant - are expressed in terms of gauge invariant and infrared stable quantities. For the renormalization of coupling constant the quark anomalous…
We compute critical exponents in a $Z_2$ symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed…
On the basis of the classical theory of envelopes, we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.
We present the natural arguments for the rationality of a recently proposed simple approach for renormalization which is based solving differential equations. The renormalization group equation is also derived in a natural way and…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
We find a new solution of the renormalization group for the Potts model with ferromagnetic random valued coupling constants. The solution exhibits universality and broken replica symmetry. It is argued that the model reaches this…
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…
Recent string theory developments suggest the necessity to understand supersymmetric gauge theories non-perturbatively, in various dimensions. In this work we show that there is a standard Hamiltonian formulation that generates a finite and…
The QCD corrections to the R_{\tau}^{12} moment of the invariant mass distribution in hadronic decays of the tau lepton are discussed. The next-to-next-to-leading order prediction is shown to be stable with respect to change of the…