Chapter

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

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/9780199573264.003.0016
Scales I: Scale sensitivity of field theory amplitudes and effective field theories

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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

Chapter.  23407 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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