are identical with those in the $A_0=0$ gauge [@CL].

In order to discuss Gupta-Bleuler quantization of this field it is convenient to introduce a generalized Klein-Gordon product of classical solutions of Eq. (\[geneq\]). We first define $$\Pi^{\mu\nu} \equiv
\frac{1}{\sqrt{-g}}\frac{\partial{\cal L}_{\rm F}}
{\partial[\nabla_\mu A_\nu]}
= -\left[F^{\mu\nu} + g^{\mu\nu} G
\right]\,,$$ where $G$ is given in Eq. (\[eqforG\]). Note that $\sqrt{-g}\,\Pi^{t\nu}$ is the canonical conjugate momentum of $A_\nu$. We write $$\Pi^{(\zeta)\mu\nu} \equiv
\left. \Pi^{\mu\nu}\right|_{A_\mu = A_\mu^{(\zeta)}}$$ for any solution $A_\mu^{(\zeta)}\equiv A_\mu^{(\lambda n ;\, \omega lm)}$. For any two (complex) solutions $A_\mu^{(\zeta)}$ and $A_\mu^{(\zeta')}$ we define $$W^\mu[A^{(\zeta)},A^{(\zeta')}]
\equiv i \left[\overline{A_\nu^{(\zeta)}}\Pi^{(\zeta')\mu\nu}
- \overline{\Pi^{(\zeta)\mu\nu}}A_\nu^{(\zeta')}\right]\,.$$ The field equations ensure that this current is conserved. As a result, the generalized Klein-Gordon inner product defined by $$(A^{(\zeta)},A^{(\zeta')}) \equiv \int_\Sigma d\Sigma_\mu
W^\mu[ A^{(\zeta)},A^{(\zeta')}]\,, \label{KGinner}$$ where $d\Sigma_\mu \equiv d\sigma\, n_\mu$, is independent of the Cauchy surface $\Sigma$ [@Fri]. (Here $d\sigma$ is the volume element of the Cauchy surface $\Sigma$ with a normal unit vector $n^\mu$.) Note that $(A^{(\zeta)},A^{(\zeta')}) =  \overline{(A^{(\zeta')},A^{(\zeta)})}$. This guarantees that the norm defined through (\[KGinner\]) is real (and positive definite for the subset of physical solutions with positive frequency). By working explicitly with the definition (\[KGinner\]), we find in general that on a $t={\rm const}$ surface $$\left( 