ABSTRACT
However, the lattice regularization of a non-Abelian gauge theory suggests another approach to quantitative calculations in strong-interaction theory. By approximating QCD by a lattice gauge theory with a nonzero lattice spacing and a finite spacetime volume, we reduce the functional integral to a finite number of bounded integrations, that is, an integral over S U (3) group m atrices for each of the finite number of links in the lattice. A lattice of size, for example, 204 allows the lattice spacing to be smaller than the size of a hadron while the full size of the lattice is much larger than a hadronic radius. Then one can compute correlation functions by evaluating the integrals numerically, by the Monte Carlo method. Since the functional integral with a finite lattice spacing is related to the original functional integral with zero lattice spacing by integrating out short-distance degrees of freedom, the lattice approximation can be systematically improved by computing the short-distance effects perturbatively, using asymptotic freedom to justify a weak-coupling analysis.*
This numerical method has now become the principal theoretical tool for quantitative calculations in hadron physics. This method currently gives the masses of the low-lying mesons and baryons to accuracies of 10-20%; it also allows the calculation of weak interaction matrix elements of hadrons at the 25% level. As computers become more powerful, this numerical method can be pushed to higher accuracy.
