Non-perturbative Renormalization in Lattice Field Theory

TL;DR

This paper reviews recent strategies for non-perturbative renormalization in lattice field theories, especially lattice QCD, focusing on momentum subtraction, finite volume schemes, and symmetry considerations.

Contribution

It provides a comprehensive overview of non-perturbative renormalization techniques and discusses their applications and current status in lattice QCD.

Findings

Analysis of momentum subtraction schemes

Application to scale-dependent renormalizations

Discussion of Symanzik's improvement program

Abstract

I review the strategies which have been developped in recent years to solve the non-perturbative renormalization problem in lattice field theories. Although the techniques are general, the focus will be on applications to lattice QCD. I discuss the momentum subtraction and finite volume schemes, and their application to scale dependent renormalizations. The problem of finite renormalizations is illustrated with the example of explicit chiral symmetry breaking, and I give a short status report concerning Symanzik's improvement programme to O($a$).