Related papers: The regulator dependence in the functional renorma…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder-Schrader formulation of quantum field theory. To this end, we devise a very general regularisation…
We prove that the functional renormalization group flow equation admits a perturbative solution and show explicitly the scheme transformation that relates it to the standard schemes of perturbation theory. We then define a universal scheme…
We study different renormalisation group flows for scale dependent effective actions, including exact and proper-time renormalisation group flows. These flows have a simple one loop structure. They differ in their dependence on the full…
Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…
We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional…
In these proceedings, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder…
We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment…
We discuss the perturbative running Yang-Mills coupling constant in the Wilsonian exact renormalization group approach, and compare it to the running coupling in the more conventional MS-bar scheme. The exact renormalization group approach…
I outline why the renormalisation group is needed to analyse the scale dependence and hence determine the power counting for effective theories of strongly interacting systems. I summarise the results of several such analyses for two- and…
We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single…
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…
A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance…
The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work treats the rigorous definition of the RG map for…
We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…
We consider here renormalizable theories without relevant couplings and present an I.R. consistent technique to study corrections to short distance behavior (Wilson O.P.E. coefficients) due to a relevant perturbation. Our method is the…
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
The non-perturbative functional renormalization group equation depends on the choice of a regulator function, whose main properties are a "coarse-graining scale" $k$ and an overall dimensionless amplitude $a$. In this paper we shall discuss…
Similarity renormalization group procedure identifies the role of bound states in the low-energy rate of change of effective coupling constant in a model Hamiltonian with asymptotic freedom.
In these notes we collect some results from several of the authors' works in order to make available a single source and show how the approximate geometric methods for regulation have been developed, and how the control design strategy has…