ABSTRACT
This chapter recalls the connection between the renormalised and unrenormalised opi Green functions to show that the Green functions of a gauge field theory change as the renormalisation scale is varied. An important process where tests of QCD are possible is the inclusive process. The Wilson expansion may be used in applications of asymptotic freedom to decay processes where the exchange of a heavy gauge boson requires us to study a product of vector or axial current operators at short distances. The chapter derives renormalisation group equations for the coefficients in the Wilson operator product expansion by first obtaining renormalisation group equations for Green functions involving some legs which are composite operators. The variation of the electromagnetic coupling constant with renormalisation scale is extremely slow and to a good approximation only the QCD coupling constant need be allowed to run.
