Exact renormalization group equations. An Introductory review

By C. Bagnuls, C. Bervillier. 2000

380 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6de1140666bd9443acdf789ef036cf79846b8dca

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In Condensed Matter Physics

In Nuclear and High Energy Physics

Citations in the corpus

The Asymptotic Safety Scenario in Quantum Gravity (2006, methodology): “In the Kadanoff–Wilson setting the bare Lagrangian contains arbitrary interaction monomials and as a consequence also nonlinear and nonlocal field reparameterizations are allowed (see [192, 21] for further discussion).”
Cosmology of the Lifshitz universe (2009, background): “These models can be studied with renormalization group (RG) techniques [54, 57, 58, 59, 60].”
An Introduction to the Nonperturbative Renormalization Group (2007, background): “d is very short whereas the ﬂow within it is slow. This is particularly clear, and has been studied in detail by Bagnuls and Bervillier, for the Z 2-invariant theories in d = 3 when they are critical.[49, 51] In this case, the RG trajectories belong to the critical surface. All of them, after a tran”