ABSTRACT
In this chapter, the previously derived expression of the photon propagator is generalised with the inclusion of Feynman diagrams taking account the insertion of fermion loops to all orders. The results of this analysis show that, in addition to the infinite constant https://www.w3.org/1998/Math/MathML" display="inline"> Z 3 discussed in Chapter 11, the definition of the renormalised charge comprises a finite https://www.w3.org/1998/Math/MathML" display="inline"> Q 2 -dependent correction. The calculation of the resulting effective coupling constant, https://www.w3.org/1998/Math/MathML" display="inline"> α ( Q 2 ) , turns out to involve the subtraction of the contribution of vacuum polarisation corresponding to a reference scale https://www.w3.org/1998/Math/MathML" display="inline"> Q 2 = μ 2 . The requirement of invariance of physical quantities on the choice of the scale https://www.w3.org/1998/Math/MathML" display="inline"> μ 2 , which provides the basis for the application of the approach based on the renormalisation group, is discussed. The derivation of the equation of Gell-Mann and Low, establishing the relation between the renormalised charges corresponding to different scales, as well as the https://www.w3.org/1998/Math/MathML" display="inline"> β function obtained from its solution at one-loop level, are illustrated.
