Lattice QCD and General Quantum Field Theory
QCD is the widely accepted theory for the strong interaction. It is formulated in the framework of quantum field theory, which describes the fundamental interactions by exchange particles. Predictive calculations are possible for phenomena at high energies, or equivalently, very short distances. Here the coupling constant is weak and perturbation theory is a useful tool. How the quarks are bound in the hadrons, however, is controlled by the large-scale behaviour of the coupling, which increases with distance. For such questions, lattice QCD is an indispensable technique, for example to compute the hadron spectrum.
Lattice QCD is QCD formulated on a discrete Euclidean spacetime lattice. LQCD preserves the fundamental character of QCD but realizes important improvements: first, the discrete spacetime lattice serves as a "regulator". A general feature of quantum field theories, and also QCD, is the occurrence of singularities. On the lattice, as long as the lattice constant a is finite, these singular quantities are rendered finite. Furthermore, the limit a → 0 is well-defined and leads to finite, so-called renormalized physical quantities. In contrast to the continuum, calculations can be performed even for high values of the coupling constant. Another advantage is that LQCD can be simulated numerically on the computer, using methods similar to those used in statistical mechanics.
Figure: Action density of the QCD vacuum from Visualizations of Quantum Chromodynamics, opens an external URL in a new window, Centre for the Subatomic Structure of Matter (CSSM) and Department of Physics, University of Adelaide, 5005 Australia. Copyright © 2003, 2004