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Phase Transitions and Renormalization Group$
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Jean Zinn-Justin

Print publication date: 2007

Print ISBN-13: 9780199227198

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199227198.001.0001

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Statistical field theory: Perturbative expansion

Statistical field theory: Perturbative expansion

(p.285) 12 Statistical field theory: Perturbative expansion
Phase Transitions and Renormalization Group

Jean Zinn-Justin

Oxford University Press

This chapter discusses the perturbative calculation of correlation or vertex functions expressed in terms of field (functional) integrals. The successive contributions to the perturbative expansion are Gaussian expectation values which can be calculated with the help, for example, of Wick′s theorem and which have a representation in the form of Feynman diagrams. It illustrates diagrammatically the relations between the first connected correlation functions and the corresponding vertex functions. It shows that the calculation of a field integral by the steepest descent method organizes the perturbative expansion as an expansion in the number of loops in the Feynman diagram representation. Finally, it defines here more generally dimensional continuation and introduces dimensional regularization. Exercises are provided at the end of the chapter.

Keywords:   Gausuan expectation values, Wick′s theorem, perturbative expansion, loop expansion, vertex functions, Feynman diagrams

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