The Schrodinger Representation for Fermions and a Local Expansion of the Schwinger Model

TL;DR

This paper develops a functional representation for fermions in the Schwinger model, deriving exact wave-functionals, revealing natural emergence of known features, and proposing a local expansion approach that could extend to numerical QCD methods.

Contribution

It introduces a novel local expansion of the Schwinger model's wave-functional and connects it to a numerical approach for higher-dimensional QCD.

Findings

Exact wave-functionals for the Schwinger model obtained.

Vacuum wave-functional does not simplify at large distances.

Expansion in local terms allows a set of algebraic equations for coefficients.

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 corresponding Schrodinger functional, which has an expansion in local terms. The functional Schrodinger 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.