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Exact Renormalization Group Equations. An Introductory Review
High Energy Physics - Theory · Submitted 4 Feb 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory.
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The abstract, sentence by sentence
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 an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. | contribution 0.97 | 0.74 | 0.08 | asserted 0.83 |
| s1 | We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. | contribution 0.63 | 0.57 | 0.10 | asserted 0.92 |
| s2 | The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. | interpretation 0.65 | 0.28 | 0.21 | asserted 1.00 |
| s3 | We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems. | limitation 1.00 | 0.60 | 0.05 | asserted 0.87 |
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The paper
Original abstract
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 an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
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References
How the literature uses it
66 arXiv papers cite this in 87 sentences
Papers citing it · 21 sentences without a confident label
Uses its method or tool 8 papers
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To tackle the non-perturbative character of these theories, we employ the functional renormalisation group (fRG) [ref] which has proven its applicability in similar frameworks.
On the phase structure of extra-dimensional gauge theories with fermions · Introduction · 0.99
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Using the functional renormalization group [ref] with the expansion of the metric field into a background field and a fluctuation one, $g_μν=g̅_μν+h_μν$, the flow of the effective action [ref] is derived.
Scaling solutions for asymptotically free quantum gravity · Flow equations · 1.00
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In this work, we employ a RG scheme that relies on a truncation of a hierarchy of flow equations derived from an exact flow equation for the scale-dependent effective action $Γ_k$ [ref] , i.e., the generating functional of one-particle irreducible (1PI) diagrams (for reviews see, e.g., Refs. [ref] ), where $k$ denotes the RG scale parameter.
Functional renormalization group approach to the Yang-Lee edge singularity · Nonperturbative functional RG · 0.93
Compares with it 1 paper
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The resulting expression for the two-point function allowed us to provide a detailed comparison of a new approach to deriving the exact flow equations of the functional renormalization group based on the 2PI effective action [ref] with the well-known approach based on the average one-particle-irreducible (1PI) effective action [ref] (see also Ref. [ref] in the context of gravity, and, e.g., Refs. [ref] for reviews).[Recently, zero-dimensional quantum field theories have also been used to study the functional renormalization group in the context of $O(N)$ models [ref] .] However, in order for this new approach to be of utility, it is necessary to formulate a procedure for extracting the $n$-point vertex functions from the 2PI effective action, and this is the focus of the present work.
Vertex functions and their flow equations from the 2PI effective action · Introduction · 0.87
Cites it as support 1 paper
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In fact, this choice is the one that minimizes the spurious breaking of reparameterization invariance due to the truncation of the exact FRG equation [ref] .
Functional Renormalization and $\overline{\text{MS}}$ · Rôle of the wave-function renormalization · 0.99
Cites it as background 51 papers
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In this section we present a brief review of Wetterich's functional renormalization group equation (FRGE) [ref] to provide the prerequisites for this paper using a Euclidean scalar field theory; detailed introductions can e.g. be found in [ref] [ref] [ref] [ref] and reviews on the application to gravity in [ref] [ref] [ref] .
Preferred foliation effects in Quantum General Relativity · The functional renormalization group equation (FRGE) · 0.96
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For our purposes, we will be interested in a relatively modern incarnation of renormalization that typically goes under the name of the Exact Renormalization Group (ERG) [ref] .
Bayesian Renormalization · Introduction · 0.97
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For a discussion of the properties of the flow equation and its application in many fields we refer to Refs. [ref] .
Scaling solutions for gauge invariant flow equations in dilaton quantum gravity · Flow equation and scaling equation · 1.00
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