Reduced phase space quantization of massive vector theory

We quantize massive vector theory in such a way that it has a well-defined massless limit. In contrast to the approach by Stuckelberg where ghost fiel ds are introduced to maintain manifest Lorentz covariance, we use reduced p hase space quantization with nonlocal dynamical variables which in the mass less limit smoothly turn into the photons, and check explicitly that the Po incare algebra is fulfilled. In contrast to conventional covariant quantiza tion our approach leads to a propagator which has no singularity in the mas sless limit and is well behaved for large momenta. For massive QED, where t he vector field is coupled to a conserved fermion current, the quantum theo ry of the nonlocal vector fields is shown to be equivalent to that of the s tandard local vector fields. An inequivalent theory, however, is obtained w hen the reduced nonlocal massive vector field is coupled to a nonconserved classical current.