Functional Schrödinger-Equation for Fermions in External Gauge Fields

Abstract

We discuss the functional Schrödinger picture for fermionic fields in external gauge fields for both stationary and time-dependent problems. We give formal results for the ground state and the solution of the time-dependent Schrödinger equation for QED in arbitrary dimensions, while more explicit results are obtained in two dimensions. For both the massless and massive Schwinger model we give an explicit expression for the ground state functional as well as for the expectation valued of energy, electric, and axial charges. We also give the corresponding results for non-abelian fields. We solve the functional Schrödinger equation for a constant external field in four dimensions and obtain the amount of particle creation. We solve the Schrödinger equation for arbitrary external fields for massless QED in two dimensions and make a careful discussion of the anomalous particle creation rate. Finally, we discuss some subtleties connected with the interpretation of the quantized Gauss constraint.