Green's-function Monte Carlo calculations on the SU(2) and U(1) lattice gauge theories

Abstract

An application of the Green's-function Monte Carlo method to the Hamiltonian formulation of the SU(2) and U(1) lattice gauge theories is described. The Green's function is that of a diffusion process in the gauge group space. A small-step approximation of the diffusion distribution is used in actual calculations. Also, a variance reduction technique is implemented, importance sampling with a disordered trial wave function optimized by the variational principle. The results of computations are reported for a 3\ifmmode\times\else\texttimes\fi{}3\ifmmode\times\else\texttimes\fi{}3 spatial lattice. The quantities computed are the ground-state energy and the expectation value of the magnetic energy, as a function of the gauge coupling constant. The results are compared to variational estimates and to weak-coupling perturbation theory.