THE SCHRÖDINGER REPRESENTATION FOR FERMIONS AND A LOCAL EXPANSION OF THE SCHWINGER MODEL

Abstract

We discuss the functional representation of fermions, and obtain exact expressions for wave-functionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations, the vacuum wave-functional does not simplify at large distances, but it may be reconstructed as a large time limit of the Schrödinger functional, which has an expansion in local terms. The functional Schrödinger equation reduces to a set of algebraic equations for the coefficients of these terms. These ideas generalize to a numerical approach to QCD in higher dimensions.