The chapter begins by introducing basic concepts of perturbative renormalization; strategies for all order proofs of renormalizability are explained without detailed proofs. Next the renormalization group equations in QCD are derived, and perturbative running couplings and masses are introduced. Renormalization of composite operators, Ward-Takahashi identities and operator product expansions are briefly discussed. Finally non-perturbative renormalization using a lattice regularization is presented, and the recursive finite size method to connect high and low energy scales is explained. The second half of the chapter considers the nature of lattice artifacts and the conjecture of their description by Symanzik's effective action. Symanzik improved lattice actions are described for Yang-Mills theory and QCD with Wilson fermions including improvement of composite operators. In the final chapter other types of improved actions are briefly discussed, in particular perfect actions, Neuberger's overlap action and twisted mass QCD.
Keywords: Renormalization; non-perturbative; running couplings; lattice artifacts; improved actions
Chapter. 31647 words. Illustrated.
Subjects: Mathematical and Statistical Physics
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