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

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

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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