  We consider the topological gauged WZW model in the generalized momentum
representation. The chiral field $g$ is interpreted as a counterpart of the
electric field $E$ of conventional gauge theories. The gauge dependence of wave
functionals $\Psi(g)$ is governed by a new gauge cocycle $\phi_{GWZW}$. We
evaluate this cocycle explicitly using the machinery of Poisson
$\sigma$-models. In this approach the GWZW model is reformulated as a Schwarz
type topological theory so that the action does not depend on the world-sheet
metric. The equivalence of this new formulation to the original one is proved
for genus one and conjectured for an arbitrary genus Riemann surface. As a
by-product we discover a new way to explain the appearance of Quantum Groups in
the WZW model.
