Quantum Gauge Invariant Formalism of the Schwinger Model: Gaugeon Theory of the Schwinger Model

Abstract

We consider the problem of restoring gauge invariance in the Schwinger model. For this purpose a gaugeon formalism of the model is constructed in such a way that the Landau gauge Schwinger model interacts with the gaugeon system only through the gauge fixing term. We introduce two more gaugeon fields and their conjugates in addition to the usual ones to compose time independent generators canonically transforming constituent fields. We make use of canonical transformations of the constituent fields in order to transform the Landau gauge operator solution into solutions in any other gauges. Gauge symmetry is restored because the canonical transformations mix the coupled system without changing Green functions. This is contrasted with the fact that we can change gauges without intro­ ducing gaugeon fields by making use of spectrum changing canonical transformations which, however, do not preserve gauge invariance because of time dependent generators.