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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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Dimensional Regularization, Minimal Subtraction: RG Functions

Dimensional Regularization, Minimal Subtraction: RG Functions

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter introduces the concept of renormalization by minimal subtraction, within the framework of dimensional regularization. It first discusses the structure of renormalization constants and renormalization group functions β(g), η(g), η2(g), and then shows that it is specially simple in the minimal subtraction scheme. It performs explicit calculations at two-loop order first in the simple one-component φ4 field and then in an N-component field theory with a general four-field interaction. These calculations will be useful for the theory of Critical Phenomena. Finally, to give an example of a theory involving fermions, the renormalization group (RG) functions are calculated at one-loop order in a theory containing fermions interacting through a Yukawa-like interaction with a scalar boson: the Gross–Neveu–Yukawa model.

Keywords:   renormalization group functions, two-loop order, scalar bosons, fermions, Gross–Neveu–Yukawa model

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