Application of the Green's function Monte Carlo method to Hamiltonian lattice field theories

The Green's function Monte Carlo (GFMC) method is adapted for application to Hamiltonian lattice gauge theories, and is applied to the SU(2) and U(1) models. The method is a Monte Carlo method for finding the ground state of a quantum-mechanical system with many degrees of freedom, by iteration of an integral equation of which the ground state is an eigenstate. An interesting aspect of the method is the use of an importance sampling technique that makes use of variational wave functions to reduce fluctuations and accelerate convergence of GEMC estimates of various quantities. The calculations were restricted by the availability of computer time, to estimates of simple quantities, the ground state energy per plaquette and the mean plaquette field, on a small lattice (3 x 3 x 3). There is no difficulty, subject to the availability of computer time, in computing other quantities or in using larger lattices. The results are interpreted in terms of the phase structure of the two groups; the SU(2) model exists in a single quark confining phase for all values of the coupling constant whereas the U(1) model in 3 + 1 dimensions undergoes a phase transition from a confining phase at strong coupling (g2 → infinity) to a non-confining phase at weak coupling (g2 → 0)