Aspects of the functional renormalisation group. (English) Zbl 1132.81041

Pawlowski, Jan M.

Ann. Phys. 322, No. 12, 2831-2915 (2007).

The renormalization group (RG) was devised within quantum field theory long time ago by Stueckelberg and Peterman, then applied to scaling transformations by Gell-Mann and Low. Its modern functional formulation owes much to the work of Callan and Symanzik in the 1970s. The present article gives an extensive overview of recent developments with regard to the general structure of the functional RG, some of these results are due to previous work of Pawlowski. The author suggests that they might be useful in applications, in particular in gauge theories, since they allow him to directly compute the evolution of observables. More generally, he studies flows of \(N\)-point correlation functions and their one-parameter reductions, the Dyson-Schwinger equation and Slavnov-Taylor identities. One promising application concerns possible renormalization schemes for \(N\)-particle irreducible effective actions generalizing the BPHZ renormalization scheme. The reader will not be surprised to find almost 200 cited articles in the References.

Reviewer: Gert Roepstorff (Aachen)

MSC:

81T17	Renormalization group methods applied to problems in quantum field theory
81T16	Nonperturbative methods of renormalization applied to problems in quantum field theory
81T13	Yang-Mills and other gauge theories in quantum field theory

Keywords:

renormalization group; renormalization; parameter evolution; gauge theories

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