Monte Carlo study of screening versus confinement in the massless and massive schwinger model

Abstract

Using Monte Carlo methods, we study the q potential in the massless and massive Schwinger model. The calculation is carried out in the bosonized version of the theory. Two different techniques for calculating the potential are discussed: the conventional Wilson loop approach, and the direct extraction of the potential from the ground state expectation value of the hamiltonian. The latter method turns out to be the more reliable. The results agree very well with the exact expressions in the massless Schwinger model, and also rather well with the semiclassical results for the massive case. We also calculate a number of other quantities of interest, such as correlation functions and expectation values of the fields, and compare them with exact and approximate results wherever available.