  We calculate the divergent part of the one-loop effective action in curved
spacetime for a particular class of second-order vector field operators with a
degenerate principal part. The principal symbol of these operators has the
structure of a longitudinal projector. In this case, standard heat-kernel
techniques are not directly applicable. We present a method which reduces the
problem to a nondegenerate scalar operator for which standard heat-kernel
techniques are available. Interestingly, this method leads to the
identification of an effective metric structure in the longitudinal sector. The
one-loop divergences are compactly expressed in terms of invariants constructed
from this metric.
