1.2.2 Renormalization The tricky subject of renormalization is dealt with in many textbooks [14,15] and is the result of efforts made in the 1940s when it was realised that simple calculations, even in QED, resulted in divergent integrals. It is now accepted that these divergences, if finite in number ∗ , can be reabsorbed into the pa- rameters of the Lagrangian. Hence quantities such as the quark mass, m , the QCD coupling constant, g , and the field strengths, A$_{µ}$ , as they appear in the Lagrangian in equation (1.1) are infinite. These quantities are called the bare values, and when we speak of the quark mass, QCD coupling con- stant etc. we are actually referring to the redefined renormalized quantities. To properly construct a systematic method of renormalization, we have to define a renormalization scale which is the energy at which we define our renormalized quantities ( m,g,A$_{µ}$ ). We then see what happens to these quantities as we vary the energy scale at which we are working. It turns out that the quantities vary as we change the energy scale. What must be remembered at all times is that the physics is independent of our choice of renormalization scale: experimentally measurable quantities are com- pletely blind to which renormalization scheme the theorist has chosen. The implication of this statement is explored in the following section, via the renormalization group equation. The first step towards calculating hadron masses, decay constants and cross- sections from (1.1) is the calculation of correlation functions. In fact this is 1.2.3 The Renormalization Group Equation $^{∗}$A theory is, by definition, renormalizable, if there are only a finite number of diver- gences. If there are an infinite number, the theory is said to be non-renormalizable. For details on how we know whether a theory is renormalizable or not, see [14] 6