The Problem Of Scales: Renormalization and All That

Abstract

I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to infinity, (b) the renormalization group, which is used to relate phenomena on different scales, (c) the operator product expansion, which shows how to obtain the asymptotics of amplitudes when some of its external momenta approach infinity.