Related papers: The Exact Renormalization Group
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
Wilson's approximation scheme of RG recursion formula dropping momentum dependence of the propagators is applied to large-$N$ vector and matrix models in dimensions $2<d<4$ by making use of their exact solutions in zero dimension. In spite…
We collect a number of facts and conjectures concerning Whitham theory and the renormalization group. Some explicit relations and problems are indicated in the context of N=2 susy Yang-Mills.
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the…
I describe an application of Wilson Renormalization group to the real time formalism of finite temperature field theory. The approach has two nice features: 1) the RG flow equations describe non-perturbatively the effect of thermal…
We report on particle physics applications of the renormalization group equation of Newton's constant.
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a few technical developments that followed the original works…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method.…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
This paper surveys some results and methods in topological transformation groups.
We propose a gauge invariant formulation of the exact renormalization group equation for nonsupersymmetric pure U(N) Yang-Mills theory, based on the construction by Tim Morris. In fact we show that our renormalization group equation amounts…
We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show…
New proves of decoupling of massive fields in several quantum field theories are derived in the effective Lagrangian approach based on Wilson renormalization group. In the most interesting case of gauge theories with spontaneous symmetry…
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of quantum gravity in arbitrary dimensions. Renormalization group flow diagrams are presented for the three-dimensional and four-dimensional…