FUNCTIONAL SCHRODINGER-EQUATION FOR FERMIONS IN EXTERNAL GAUGE-FIELDS

We discuss the functional Schrodinger picture for fermionic fields in external gauge fields for both stationary and time-dependent problems. We give formal results for the ground stale and the solution of the t ime-dependent Schrodinger equation for QED in arbitrary dimensions, wh ile more explicit results are obtained in two dimensions. For both the massless and massive Schwinger model we give an explicit expression f or the ground state functional as well as for the expectation valued o f energy, electric, and axial charges. We also give the corresponding results for non-abelian fields. We solve the functional Schrodinger eq uation for a constant external field in four dimensions and obtain the amount of particle creation. We solve the Schrodinger equation for ar bitrary external fields for massless QED in two dimensions and make a careful discussion of the anomalous particle creation rate. Finally, w e discuss some subtleties connected with the interpretation of the qua ntized Gauss constraint. (C) 1994 Academic Press, Inc.