Non-perturbative renormalization of QCD

Abstract

In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the scale-dependence of renormalized quantities is explained. An important ingredient in the practical applications is the Schrödinger functional. It is introduced and its renormalization properties are discussed. Concerning applications, the computation of the running coupling and the running quark mass are covered in detail and it is shown how the $\Lambda$-parameter and renormalization group invariant quark mass can be obtained. Further topics are the renormalization of isovector currents and non-perturbative Symanzik improvement.

49 pages, lectures at Schladming-97

References in corpus (1)

• O(a) improved lattice QCD

Cited by in corpus (12)

• Computation of the strong coupling in QCD with two dynamical flavours
• Studying the gradient flow coupling in the Schrödinger functional
• The gradient flow coupling in the Schrödinger Functional
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Two-Loop Computation of the Schroedinger Functional in Pure SU(3) Lattice Gauge Theory
• Lattice determinations of the strong coupling
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Lattice studies of QCD-like theories with many fermionic degrees of freedom
• Scaling investigation of renormalized correlation functions in O(a) improved quenched lattice QCD
• Lattice gauge theory in technicolor
• Linking infrared and ultraviolet parameters of pion-like states in strongly coupled gauge theories
• Memory efficient finite volume schemes with twisted boundary conditions