Chapter

Scales III: Short-distance structure of quantum field theory

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print August 2012 | ISBN: 9780199573264
Published online January 2013 | e-ISBN: 9780191743313 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199573264.003.0018
Scales III: Short-distance structure of quantum field theory

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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

Chapter.  25216 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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