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Quantum Field Theory and Critical Phenomena$
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Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

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Introduction to Renormalization Theory. Renormalization Group Equations

Introduction to Renormalization Theory. Renormalization Group Equations

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter presents the essential steps of the proof of the renormalizability of a simple scalar field theory: the φ4 field theory in d = 4 dimensions. However, all the fundamental difficulties of renormalization theory are already present in this particular example and it will eventually become clear that the extension to other theories is not difficult. The elegant presentation of Callan (Les Houches 1975) is followed, which allows renormalizability and renormalization group (Callan–Symanzik) equations to be proved at once. This presentation is specially suited to the chapter's general purpose since a large part of this work is devoted to applications of renormalization group (RG). Moreover, it emphasizes already at this technical level the equivalence between renormalizability and the existence of a renormalization.

Keywords:   renormalizability, field theory, Callan–Symanzik equations, renormalization group

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