Reduced phase space quantization of massive vector theory

TL;DR

This paper presents a reduced phase space quantization method for massive vector fields that smoothly transitions to the massless photon case, avoiding singularities and maintaining Poincare invariance.

Contribution

It introduces a nonlocal reduced phase space quantization approach that differs from St"uckelberg's method, ensuring a well-behaved massless limit and preserving Lorentz covariance.

Findings

Propagator free of massless limit singularities

Equivalent to standard local vector field theory when coupled to conserved currents

Provides a consistent quantization scheme with smooth massless transition

Abstract

We quantize massive vector theory in such a way that it has a well-defined massless limit. In contrast to the approach by St\"uckelberg where ghost fields are introduced to maintain manifest Lorentz covariance, we use reduced phase space quantization with nonlocal dynamical variables which in the massless limit smoothly turn into the photons, and check explicitly that the Poincare algebra is fullfilled. In contrast to conventional covariant quantization our approach leads to a propagator which has no singularity in the massless limit and is well behaved for large momenta. For massive QED, where the vector field is coupled to a conserved fermion current, the quantum theory of the nonlocal vector fields is shown to be equivalent to that of the standard local vector fields. An inequivalent theory, however, is obtained when the reduced nonlocal massive vector field is coupled to a nonconserved classical current.