Ultralocal fields and their relevance for reparametrization-invariant quantum field theory

Reparametrization-invariant theories have a vanishing Hamiltonian and enfor ce their dynamics through a constraint. We specifically choose the Dirac pr ocedure of quantization before the introduction of constraints. Consequentl y, for field theories, and prior to the introduction of any constraints, it is argued that the original field operator representation should be ultral ocal in order to remain totally unbiased toward those field correlations th at will be imposed by the constraints. It is shown that relativistic free a nd interacting theories can be completely recovered starting from ultraloca l representations followed by a careful enforcement of the appropriate cons traints. In so doing all unnecessary features of the original ultralocal re presentation disappear. The present discussion is germane to a recent theory of affine quantum grav ity in which ultralocal field representations have been invoked before the imposition of constraints.