vector. It is immediately evident that this is impossible since there is an insufficient number of four vectors ($P$ and $q$) to combine with the tensor $\epsilon _{\mu \nu \alpha \beta }$ to form an axial vector. The solution to (\[IBS\]) must therefore have the general form $$\Gamma _{\mu }(P,q)={\bf 1}\Lambda ^{(1)}_{\mu }(P,q)+i\gamma _{\nu
}\Lambda ^{(2)}_{\nu \mu }(P,q)+i\gamma _5\gamma _{\nu }\epsilon _{\mu
\nu \alpha \beta }P_{\alpha }q_{\beta }\eta ^{-2}\Lambda
^{(3)}(P,q),\label{2.6}$$ where the matrix structure is now explicit and the quantities $\Lambda
^{(i)}$ are dimensionless functions with Lorentz structure indicated by their indices. The constant $\eta $ has dimension of (length)$^{-1}$ and is associated with the infrared strength of the gluon two-point function.

The further reduction of the $\Lambda ^{(i)}$ to a set of invariant functions is achieved through the use of the symmetry transformations of the vertex $\Gamma _{\mu }(P,q)$ under $\gamma _5$; charge conjugation, ${\cal C}=\gamma _2\gamma _4$; and parity, ${\cal
P}=\gamma _4$. The transformation properties are determined directly from the inhomogeneous Bethe-Salpeter equation (\[IBS\]) and are given by $$\begin{aligned}
\gamma _5\Gamma _{\mu }(P,q)\gamma _5 &=& -\Gamma _{\mu }(-P,-q)\nonumber \\
{\cal C}\Gamma _{\mu }(P,q){\cal C}^{-1}&=& -\Gamma _{\mu
}(-P,q)^t\label{2.7}\\
{\cal P}\Gamma _{\mu }(P,q){\cal P}^{-1}&=& \omega _{\mu \nu }\Gamma
_{\nu }(P_4;-{\bf 