An Introduction to the Nonperturbative Renormalization Group

Abstract

An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive overview of the subject but rather to insist on conceptual aspects and to explain in detail the main technical steps. It should be taken as an introduction to more advanced readings.Comment: 56 page

Infrared dynamics in de Sitter space from Schwinger–Dyson equations

“…To discuss the above results further, we now specify the mass parameter (6) which characterizes the propagatorĜ M entering the two-loop self-energy (16). As mentioned previously, for m 2 dS ≤ 0 perturbation theory is ill-defined and one has to resum a mass.…”

“…In the following we shall need the low momentum behavior of the statistical and spectral components of the self-energy (16). Introducing an arbitrary scale µ 1 to separate between super and subhorizon modes, one can show, using the method developed in Ref.…”

“…Indeed, such corrections become relevant at very large values of |x| involved in convolution integrals. In particular, we emphasize the e −2ǫ|x| term in (20), which is a nontrivial contribution from modes close to the horizon in the loop integral (16) [see Appendix A] and which plays a crucial role in obtaining the analytical solution below.…”

“…Serreau ) Various methods have been developed over the years to deal with similar issues in flat space, e.g., near a critical point [16], for bosonic degrees of freedom at very high temperatures [17] or for systems out of equilibrium [18]. In recent years, a lot of activity has been devoted to adapt these techniques to nontrivial cosmological spaces, mainly for scalar fields.…”

Long-range and many-body effects in coagulation processes

“…We specialize the treatment to the coagulation process and put particular emphasis on the derivation of the kinetic equation. For authoritative reviews and more detailed accounts on the general topic the reader is referred to [22][23][24]26,27].…”