Nonperturbative renormalization flow in quantum field theory and statistical physics
Abstract
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Nonperturbative solutions follow from approximations to the general form of the coarsegrained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O( N)symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the secondorder phase transitions, including the KosterlitzThouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquidgas transition. Universal features of firstorder phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the hightemperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular, we explore chiral symmetry breaking and the hightemperature or highdensity chiral phase transition in quantum chromodynamics using models with effective fourfermion interactions.
 Publication:

Physics Reports
 Pub Date:
 June 2002
 DOI:
 10.1016/S03701573(01)000989
 arXiv:
 arXiv:hepph/0005122
 Bibcode:
 2002PhR...363..223B
 Keywords:

 High Energy Physics  Phenomenology;
 Condensed Matter
 EPrint:
 178 pages, appears in Physics Reports