QUANTIZATION OF ANOMALOUS GAUGE FIELD-THEORY AND BRST-INVARIANT MODELS OF 2-DIMENSIONAL QUANTUM-GRAVITY

We analyze the problems with the so-called gauge-invariant quantizatio n of the anomalous gauge field theories originally due to Faddeev and Shatashvili (FS). Our analysis is a generalization of the FS method, w hich allows us to construct a series of classically equivalent theorie s that are nonequivalent at the quantum level. We prove that these cla ssical theories are all consistent with the BRST invariance of the ori ginal gauge symmetry with a suitably augmented field content. As an ex ample of such a scenario, we discuss the class of physically distinct models of two-dimensional induced gravity, which are a generalization of the David-Distler-Kawai model.