The theory of the strong interactions on a space-time lattice

Quantum Chromodynamics has been accepted as the theory of the strong interactions for more than thirty years, ever since the discovery of asymptotic freedom by Gross, Politzer and Wilczek, whose work was recognized with the 2004 Nobel Prize. Despite many successful quantitative predictions for high-energy processes, applications of QCD to strongly-coupled, low-energy hadronic physics, including such basic quantities as the proton mass, have historically been much less successful. A space-time lattice discretization of QCD (proposed by Ken Wilson the year after asymptotic freedom) lends itself to direct numerical simulation, but the enormous computational burden of lattice QCD has, until recently, precluded accurate simulations of the full theory. Happily, dramatic improvements in the predictive power of lattice QCD have occurred in the past few years, due to major theoretical progress in our understanding of lattice quantum field theories. These developments are having a significant impact, including the use of lattice QCD to constrain the search for physics beyond the so-called standard model. This talk will give a conceptual review of the theory of QCD at high and low energies and the new developments in lattice QCD.