Short Course Description
Lattice field theory defines a quantum field theory with a space-time cutoff from the beginning. This permits the application of many manipulations beyond the reach of Feynman-diagram perturbation theory, as well as numerical calculations of non-perturbative properties; the continuum limit is taken at the end of any calculation. The course introduces the lattice formulation of quantum chromodynamics and related field theories; its application to the non-perturbative problems of quark confinement, chiral symmetry breaking, and phase transitions at nonzero temperature; use of the renormalization group in taking the continuum limit. It will cover the subtleties of defining fermionic fields on a lattice. The bulk of modern work is numerical, using supercomputers, and so numerical Monte Carlo methods will be described, as well as current subjects such as the calculation of scattering amplitudes.