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The Conceptual Framework of Quantum Field Theory$
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Anthony Duncan

Print publication date: 2012

Print ISBN-13: 9780199573264

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199573264.001.0001

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Scales III: Short-distance structure of quantum field theory

Scales III: Short-distance structure of quantum field theory

Chapter:
(p.662) 18 Scales III: Short-distance structure of quantum field theory
Source:
The Conceptual Framework of Quantum Field Theory
Author(s):

Anthony Duncan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573264.003.0018

This chapter discusses one of the most fertile manifestations of scale separation in field theory: the Wilson operator product expansion (OPE), which provides a precise characterization of the short-distance asymptotics of field theory amplitudes in terms of factorized products of ‘short-’ and ‘long-’distance terms. The useful application of the OPE in particular processes depends on the presence and structure of mass singularities in the relevant amplitudes. The role of the renormalization group in studying high-energy (or short-distance) behaviour is outlined.

Keywords:   scale separation, quantum field theories, Wilson operator product expansion, field theory amplitudes, renormalization group

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