  The local momentum space method is used to study the quantized massive vector
field (the Proca field) with the possible addition of non-minimal terms. Heat
kernel coefficients are calculated and used to evaluate the divergent part of
the one-loop effective action. It is shown that the naive expression for the
effective action that one would write down based on the minimal coupling case
needs modification. We adopt a Faddeev-Jackiw method of quantization and
consider the case of an ultrastatic spacetime for simplicity. The operator that
arises for non-minimal coupling to the curvature is shown to be non-minimal in
the sense of Barvinsky and Vilkovisky. It is shown that when a general
non-minimal term is added to the theory the result is not renormalizable with
the addition of a local Lagrangian counterterm.
