  In the conformal-gauge two-dimensional quantum gravity, the solution obtained
by the perturbative or path-integral approach is compared with the one obtained
by the operator-formalism approach. Treatments of the anomaly problem in both
approaches are different. This difference is found to be essentially caused by
the fact that the perturbative or path-integral approach is based on the
T*-product (covariantized T-product), which generally violates field equations.
Indeed, this fact induces some extra one-loop Feynman diagrams, which would not
exist unless a nonzero contribution arose from a zero field. Some demerits of
the path-integral approach are explicitly demonstrated.
