CONFORMALLY INVARIANT PATH-INTEGRAL FORMULATION OF THE WESS-ZUMINO-WITTEN-]LIOUVILLE REDUCTION

The path integral description of the Wess-Zumino-Witten --> Liouville reduction is formulated in a manner that exhibits the conformal invari ance explicitly at each stage of the reduction process. The descriptio n requires a conformally invariant generalisation of the phase-space p ath integral methods of Batalin, Fradkin, and Vilkovisky for systems w ith first class constraints. The conformal anomaly is incorporated in a natural way and a generalisation of the Fradkin-Vilkovisky theorem r egarding gauge independence is proved. This generalised formalism shou ld apply to all conformally invariant reductions in all dimensions. A previous problem concerning the gauge dependence of the centre of the Virasoro algebra of the reduced theory is solved. (C) 1998 Elsevier Sc ience B.V.