Exact renormalization group equations. An Introductory review

  title={Exact renormalization group equations. An Introductory review},
  author={C. Bagnuls and C. Bervillier},
  journal={Physics Reports},
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is… Expand

Figures from this paper

Paper Mentions

Blog Post
Non-perturbative renormalization group for simple fluids
We present a new non-perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and also in the framework of two equivalent scalar fieldExpand
Exact renormalization group equation for the Lifshitz critical point
Abstract An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivativeExpand
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general WilsonExpand
Non-perturbative renormalization group calculation of the scalar self-energy
Abstract.We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions forExpand
An Introduction to the Nonperturbative Renormalization Group
We give in these notes a short presentation of both the main ideas underlying Wilson’s renormalization group (RG) and their concrete implementation under the form of what is now called theExpand
Correlation functions in the Non Perturbative Renormalization Group and field expansion
Abstract.The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain n-point correlation functions at finite momenta isExpand
Proper time regulator and renormalization group flow
We consider some applications of the Renormalization Group flow equations obtained by resorting to a specific class of proper time regulators. Within this class a particular limit that corresponds toExpand
Revisiting the local potential approximation of the exact renormalization group equation
Abstract The conventional absence of field renormalization in the local potential approximation (LPA) — implying a zero value of the critical exponent η — is shown to be incompatible with the logicExpand
Towards an accurate determination of the critical exponents with the renormalization group flow equations
Abstract The determination of the critical exponents by means of the exact renormalizion group approach is still a topic of debate. The general flow equation is by construction scheme independent,Expand
Renormalization Theory Based on Flow Equations
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson renormalization group. I first consider massive Euclidean ϕ 4 4 -theory.Expand


The Derivative Expansion of the Exact Renormalization Group
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this methodExpand
Elements of the Continuous Renormalization Group
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exactExpand
Rapidly Converging Truncation Scheme of the Exact Renormalization Group
The truncation scheme dependence of the exact renormalization group equations is inves­ tigated for scalar field theories in three dimensions. The exponents are numerically estimated to theExpand
The Exact Renormalization Group and Approximations
We review the Exact Renormalization Group equations of Wegner and Houghton in an approximation which permits both numerical and analytical studies of nonperturbative renormalization flows. We obtainExpand
Exact renormalization group study of fermionic theories
Abstract The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixedExpand
Critical behavior of ϕ4-theory from the thermal renormalization group
Abstract We discuss the universal critical behavior of a selfinteracting scalar field theory at finite temperature as obtained from approximate solutions to nonperturbative renormalization group (RG)Expand
The Exact renormalization group and approximate solutions
We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff Green’s functions are given. AExpand
Ward identities and Wilson renormalization group for QED
Abstract We analyze a formulation of QED based on the Wilson renormalization group. Although the “effective lagrangian” used at any given scale does not have simple gauge symmetry, we show that theExpand
Large N and the renormalization group
Abstract In the large N limit, we show that the local potential approximation to the flow equation for the Legendre effective action, is in effect no longer an approximation, but exact - in a sense,Expand
Derivative expansion of the renormalization group in O(N) scalar field theory
We apply a derivative expansion to the Legendre effective action flow equations of O(N) symmetric scalar field theory, making no other approximation. We calculate the critical exponents η, ν, and ωExpand