INTEGRATION OVER QUASIGROUP ORBITS

A geometric treatment of the Lagrangian path integral for gauge theori es based on a closed algebra is presented. A general expression that e nsures gauge invariance of the path integral is obtained for the funct ional measure. The integral over gauge orbits is considered as an inte gral over hypersurfaces in the configuration space that are specified by an arbitrary gauge condition. A special form of the measure in the integral over the orbits is constructed by analogy with the decomposit ion of the determinant of the 4-metric in canonical gravity. The resul ts are discussed briefly in the context of operator ordering and quant um anomalies.