(\[2.16\]) along with the explicit forms of ${\cal M}$, ${\cal N}$ and $b$ are given in the appendix. The equation (\[2.16\]) contains the same information as the transverse component of the inhomogeneous Bethe-Salpeter equation (\[IBS\]); to this point, no approximations have been made. To proceed further requires the specification of the gluon two-point function, $D$.

The homogeneous Bethe-Salpeter equation
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The solutions of the homogeneous Bethe-Salpeter equation, (\[BS\]), describe the coupling of a $q\bar{q}$ vector bound state to a quark, and thereby provide information about the internal dynamics of the bound state. Although these solutions can be obtained directly from the coefficient functions, $\lambda ^{T}_{i}$ of the previous section, their normalization is more readily achieved by considering the solution of the homogeneous equation. To this end, the quantity $\Omega _{\mu }(P,q)$ is decomposed as $$\Omega _{\mu }(P,q)={\bf 1}\phi ^{(1)}_{\mu
}(P,q)+\frac{i}{\sqrt{2}}\gamma _{\nu }\phi ^{(2)}_{\nu \mu
}(P,q)+\frac{i}{\sqrt{2}}\gamma _{5}\gamma _{\nu }\phi ^{(3)}_{\nu \mu
}(P,q).\label{2.17}$$ The association of the coefficients $\phi ^{(i)}$ with the coefficients $\Lambda ^{(i)}$ of (\[2.6\]) is directly observed from the relationship between the solutions to the inhomogeneous and homogeneous Bethe-Salpeter equations given in (\[pole\]). The substitution of (\[2.17\]) into the homogeneous equation (\[BS\]) allows a description in the form of 