Introduction to renormalisation group theory

BEN ZHANG; K. I. MAZZITELLO

Atlanta

Seminario; Journal Club, Georgia State University; 2019

Department of Mathematics and Statistics, Georgia State University

The condensed mater physics contains two versions of the renormalisation group (RG): the Gell-Mann-Low RG and the Wilson RG. In critical phenomena, the use of the former is based upon perturbation theory, whilst the latter has a direct geometrical interpretation and is in principle, non-perturbative. The connection between the two versions is by no means obvious. In this seminar we will see that renormalisation has a direct physical interpretation, and may be easily understood wihout the technical complications of quantum field theory. The RG was originally developed to treat critical phenomena and shifted away from phase transitions and field theory, towards non-equilibrium phenomena. One active field of research is the study of dynamical phenomena where there is a fluctuating noise source present. The RG have been used to study how these fluctuations scale in both space and time. Basically, renormalisation is a coarse-graining procedure in which fine detail are smoothed.