THE REGULARIZED BRST JACOBIAN OF PURE YANG-MILLS THEORY

The jacobian for infinitesimal BRST transformations of path integrals for pure Yang-Mills theory, viewed as a matrix 1+DELTAJ in the space of Yang-Mills fields and (anti)ghosts, contains off-diagonal terms. Naively, the trace of DELTAJ vanishes, being proportional to the trace of the structure constants. However, the consistent regulator R, constructed from a general method, also contains off-diagonal terms. An explicit computation demonstrates that the regularized jacobian tr DELTAJ exp (- R/M2) for M2 --> infinity is the variation of a local counter-term, which we give. This is a direct proof, at the level of path integrals, that there is no BRST anomaly.