The renormalization group and the ɛ expansion
Abstract
The modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory. The expansion in ɛ = 4 d is explained [ d is the dimension of space (statistical mechanics) or spacetime (quantum field theory)]. The emphasis is on principles, not particular applications. Sections 18 provide a selfcontained introduction at a fairly elementary level to the statistical mechanical theory. No background is required except for some prior experience with diagrams. In particular, a diagrammatic approximation to an exact renormalization group equation is presented in sections 4 and 5; sections 68 include the approximate renormalization group recursion formula and the Feyman graph method for calculating exponents. Sections 1013 go deeper into renormalization group theory (section 9 presents a calculation of anomalous dimensions). The equivalence of quantum field theory and classical statistical mechanics near the critical point is established in section 10; sections 1113 concern problems common to both subjects. Specific field theoretic references assume some background in quantum field theory. An exact renormalization group equation is presented in section 11; sections 12 and 13 concern fundamental topological questions.
 Publication:

Physics Reports
 Pub Date:
 August 1974
 DOI:
 10.1016/03701573(74)900234
 Bibcode:
 1974PhR....12...75W