An Introduction to the Nonperturbative Renormalization Group

  title={An Introduction to the Nonperturbative Renormalization Group},
  author={Bertrand Delamotte},
  journal={Lecture Notes in Physics},
  • B. Delamotte
  • Published 15 February 2007
  • Physics
  • Lecture Notes in Physics
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 the non-perturbative renormalization group (NPRG) or sometimes the functional renormalization group (which can be perturbative). Prior knowledge of perturbative field theory is not required for the understanding of the heart of the article. 
Renormalization: an advanced overview
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in
Renormalization group flow equations with full momentum dependence
  • J. Blaizot
  • Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2011
A particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the n-point functions is discussed, to critical O(N) models, to Bose–Einstein condensation and to finite-temperature field theory.
The Exact Renormalization Group -- renormalization theory revisited --
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative
Nonperturbative Quantum Field Theory
In this chapter, we describe nonperturbative quantum field theory in the setting of the nonperturbative renormalization group approach of Wilson-Wetterich. We start by discussing the geometric
New applications of the renormalization group method in physics: a brief introduction
  • Y. Meurice, R. Perry, S. Tsai
  • Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2011
The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics, in a way that emphasizes common themes and the universal aspects of the method.
Functional renormalization group approach to the Kraichnan model.
  • C. Pagani
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
The symmetries of the Kraichnan model are analyzed and the leading correction to the structure functions considering the renormalization of composite operators and applying the operator product expansion is derived.
Non-perturbative renormalization group approach to zero-temperature Bose systems
We use a non-perturbative renormalization group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when d≤3 and yields the
New method of the functional renormalization group approach for Yang-Mills fields
We propose a new formulation of the functional renormalization group (FRG) approach, based on the use of regulator functions as composite operators. In this case one can provide (in contrast with
The Wilson exact renormalization group equation and the anomalous dimension parameter
The non-linear way the anomalous dimension parameter has been introduced in the historic first version of the exact renormalization group equation is compared to current practice. A simple expression
Ward-Takahashi Identity for Yang-Mills Theory in the Exact Renormalization Group
We give a functional derivation of the Ward-Takahashi identity for Yang-Mills theory in the framework of the exact renormalization group. The identity realizes non-abelian gauge symmetry nontrivially


What can be learnt from the nonperturbative renormalization group
We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is
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 Wilson
A Hint of renormalization
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical
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 field
Nonperturbative renormalization group approach to the Ising model: A derivative expansion at order ∂4
On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order ∂ 4 of
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. A
Renormalization group equation for critical phenomena
An exact renormalization equation is derived by making an infinitesimal change in the cutoff in momentum space. From this equation the expansion for critical exponents around dimensionality 4 and the
Nonperturbative functional renormalization group for random-field models: the way out of dimensional reduction.
It is found that the failure of dimensional reduction and standard perturbation theory is due to the nonanalytic nature of the zero-temperature fixed point controlling the critical behavior, nonanalyticity, which is associated with the existence of many metastable states.