Note on Fujikawa's Method of Determining the Critical Dimension of the Relativistic String

摘要

Fujikawa's (1982) derivation of the critical dimension of the relativistic string in the path integral formulation is considered. It is shown that the correct prescription for choosing the functional measure is obtained by requiring standard BRST-invariance without modifications and that Fujikawa's choice of measure is not unique. A one-parameter family of BRST-invariant measures is found, even after fixing a gauge for local Weyl rescalings. Gauge independence of the resulting theory is demonstrated in the critical number of dimensions.