Resummation in hot field theories
type: Item
instance of: scholarly article
title: Resummation in hot field theories
zbMATH Open document ID: 1072.81061
author: Jens O. Andersen
author: Michael Strickland
published in: Annals of Physics
publication date: 2005-08-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-ph/0404164
review text: There has been significant progress in the understanding of finite-temperature field theory over the past decade. In this paper the progress in perturbative thermal field theory focusing on thermodynamic quantities is reviewed. There are discussed first the breakdown of naive perturbation theory (loop expansion) at finite temperature due to infrared divergences. Diagrams which are nominally of higher order in the coupling constant contribute to leading order in the interaction parts \(g\). Thus, dividing the euclidean Lagrangian of a scalar field in a free part proportional to \(g^0\) and an interaction part proportional to \(g^2\), and calculating radiative corrections in a loop expansion which is equivalent to a power series in \(g^2\) (that means in \(\phi^4\)-interaction), one finds that the perturbative expansion breaks down at finite temperature and the week coupling expansion becomes an expansion in \(g\) rather than in \(g^2\). Thus, a consistent perturbative expansion requires the resummation of an infinite subset of diagrams from all orders of perturbation theory. The Braaten-Pisarski resummation approach is such a consistent expansion, it can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of \(g\). However, it turns out that the weak coupling expansion for thermodynamic quantities is useless unless the coupling constant is very small. In the paper it is shown that the perturbative expansion of the free energy for both simple scalar field theories and QCD have a very small, if not vanishing, radius of convergence. In the case of QCD this makes the resulting expansion useless at phenomenologically relevant temperatures. Then it is shown that dimensional reduction (DR) and effective field theory methods can provide an efficacious way of organizing weak-coupling calculations. By combining them with nonperturbative methods such as lattice gauge theory, the long-standing problem of calculating …
Mathematics Subject Classification ID: 81V05
Mathematics Subject Classification ID: 81T15
Mathematics Subject Classification ID: 81V10
Mathematics Subject Classification ID: 81V35
Mathematics Subject Classification ID: 82B30
zbMATH DE Number: 2189465
zbMATH Keywords: quark-gluon plasma
zbMATH Keywords: finite temperature field theory
zbMATH Keywords: quantum chromodynamics
zbMATH Keywords: perturbation theory
zbMATH Keywords: resummation of perturbation theory
zbMATH Keywords: thermodynamics
reviewed by: Claudia-Veronika Meister
MaRDI profile type: Publication
OpenAlex ID: W2049773438
arXiv ID: hep-ph/0404164
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DOI: 10.1016/J.AOP.2004.09.017
description: scientific article