(q^2)\int d^4P\Phi _{a}^{\mu }(P,-q)\Phi
_{a}^{\nu }(P,q)\nonumber \\
&\stackrel{q^2\sim -M_V^2}{=} & \left(\delta _{\mu \nu}-\frac{q_{\mu
}q_{\nu }}{q^2}\right) \left(q^2+M_V^2\right) Z(q^2).\label{2.20}\end{aligned}$$ The last line in (\[2.19\]) follows from the fact that the on-mass-shell eigenfunctions, $\Phi _{a}^{\mu }$, contain only components transverse to the center-of-mass momentum $q_{\mu }$. The (dimensionless) wavefunction renormalization constant $Z(q^2)$ can be absorbed into the Bethe-Salpeter amplitudes by defining $\hat{\Phi
}_{a}^{\nu }\equiv \Phi _{a}^{\nu }/\sqrt{Z(-M_V^2)}$. The normalization condition can then be written explicitly as $$\left. \frac{1}{3}\int d^4Pd^4K\hat{\Phi }_{a}^{\nu
}(P,-q)\frac{\partial }{\partial q_{\mu }}\left[ \Delta
^{-1}_{ab}(P,K;q)\right] \hat{\Phi }_{b}^{\nu }(K,q)\right| _{q^2=-M_V^2}
=2q_{\mu },\label{2.21}$$ which is the standard result[@iz]. In terms of the properly normalized Bethe-Salpeter amplitude, the relationship to the QPV given in (\[pole\]) now reads $$\Gamma _{\mu }(P,q) \approx
\frac{M_V^2}{q^{2}+M_{V}^{2}}\frac{\hat{\Omega }_{\mu }(P,q)}{f_V},\label{2.22}$$ where $f_V\equiv 1/\sqrt{Z(-M_V^2)}$ is the effective coupling of the vector meson to the photon.

A simple model
==============

Traditional descriptions of quark confinement are based on a potential between quarks, in an appropriate color combination, which rises with increasing separation (to infinity in the absence of pair creation). Explored here is the notion that this effect may be in part due to the interaction of quarks (or more generally colored objects) with the vacuum. In particular, that confinement is manifest in 