The factor-ordering problem must be regulated

Three points are stressed concerning the factor-ordering problem of canonical quantum gravity. First, the problem is real; dimensional regularization in the covariant formalism permits us to systematically ignore it, but does not provide a resolution. Second, no resolution of the problem is possible until the naive constraint algebra is first regulated to remove divergences arising from singular operator products. This point is underlined with an example from the literature. Third, we argue that whatever regulation technique is employed should respect general coordinate invariance or some analog of it. Although the traditional variables of canonical quantum gravity are used, our conclusions apply with equal force to the new variables proposed by Ashtekar.