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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 I: Scale sensitivity of field theory amplitudes and effective field theories

Scales I: Scale sensitivity of field theory amplitudes and effective field theories

Chapter:
(p.569) 16 Scales I: Scale sensitivity of field theory amplitudes and effective field theories
Source:
The Conceptual Framework of Quantum Field Theory
Author(s):

Anthony Duncan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573264.003.0016

This chapter discusses various aspects of scale separation: the critical role it plays in leading to quantitative predictions at accessible energy scales; the introduction of regularization techniques to quantify and simplify the study of scale sensitivity; the relevance of power counting methods in local quantum field theories; the extremely important concept of effective Lagrangians; and the classification of operators into relevant, marginal, and irrelevant on the basis of their scaling behaviour. Here the point of view first introduced by Wilson in the 1970s — whereby the physics of a system is described in terms of an ‘effective Lagrangian’ which incorporates, via a set of ‘renormalization group’ equations, the behaviour over a strictly limited range of distance (or energy) scales — moves to the centre of the discussion of quantum field theory.

Keywords:   scale separation, quantum field theory, Lagrangians, effective Lagrangian

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