Hamiltonian Eigenvalues for Lattice Gauge Theories

Abstract

A brief review is presented of Lanczos sparse matrix techniques in solving Hamiltonian lattice gauge theory. The Hamiltonian approach gives direct access to many measurable quantities (such as masses) in quantum field theory. A brute force approach (initiated by Hamer and Barber) of exactly solving a spatially restricted system proves extremely powerful when coupled with scaling and renormalisation methods. The simple Lanczos (tri-) diagonalisation scheme provides a practical way of performing the exact calculation on restricted systems. The matrices are large, speed is required but accuracy cannot be sacrificed. Some successful applications are reviewed.