Related papers: Interplay Between Approximation Theory and Renorma…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
This book provides an introduction to a renormalisation group method in the spirit of that of Wilson. It starts with a concise overview of the theory of critical phenomena and the introduction of several tools required in the…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
This paper is the fourth in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The third paper in the series presents a perturbative…
The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point…
Recently a number of analytic prescriptions for computing the non-linear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus…
The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…
we show there exists a mathematically consistent framework in which the Renormalization Program can be understood in a natural manner. The framework does not require any violations of mathematical rigor usually associated with the…
The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At…
Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
In the O(N) model for the large N expansion one needs resummation which makes the renormalization of the model difficult. In the paper it is discussed, how can one perform a consistent perturbation theory at zero as well as at finite…
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…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two…