Renormalization and physical parameters

We will return to the latter diagrams when discussing in detail the eflfect of weak radiative corrections in muon decay. 

Quantitatively, the most important contributions arise either from large logarithms (e.g. terms of the form where / is a light 

Even non-theoretical readers are urged to peruse the introductory part of Chapter 20 where the idea of renormalization is explained without any detailed mathematical calculations. Nonetheless we feel it important to make some comments here on this question. 

If higher order perturbative effects are calculated using the Lagrangian couplings given in (5.1.1) and (5.1.3) in which the parameters e and sin iv are considered as fixed numbers, many diagrams yield infinite answers and the theory has to be renormalized. 

In books on field theory one starts with the Lagrangian in which all the parameters, coupling and masses are called bare parameters and are labelled eo, 50, lo etc. These bare parameters are not what one measures to make the theory finite they have to be allowed to depend on a cut-off A temporarily introduced into the theory and most of them become infinite when at the end one lets A - 00. What A is depends upon the method of regularization . Thus A may literally be a cut-off, i.e. the upper limit of some loop integration, or it may be 1/e where one uses dimensional regularization to work in 4 — e dimensions and at the end lets c 0. 

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