which all the Green’s functions are decomposed together with the coefficients of the projection tensors which project out each specific amplitude.

Preliminaries.
==============

In this section we recall the background to the problem and the calculational set-up. First, the various operators we will be considering, which are gauge invariant, are $$\begin{aligned}
S & \equiv & \bar{\psi} \psi ~, \nonumber \\
V & \equiv & \bar{\psi} \gamma^\mu \psi ~, \nonumber \\
T & \equiv & \bar{\psi} \sigma^{\mu\nu} \psi ~, \nonumber \\
W_2 & \equiv & {\cal S} \bar{\psi} \gamma^\mu D^\nu \psi ~, \nonumber \\
\partial W_2 & \equiv & {\cal S} \partial^\mu \left( \bar{\psi} \gamma^{\nu}
\psi \right) ~, \nonumber \\
W_3 & \equiv & {\cal S} \bar{\psi} \gamma^\mu D^\nu D^\sigma \psi 
\nonumber \\
\partial W_3 & \equiv & {\cal S} \partial^\mu \left( \bar{\psi} \gamma^\nu
D^\sigma \psi \right) ~, \nonumber \\
\partial \partial W_3 & \equiv & {\cal S} \partial^\mu \partial^\nu \left(
\bar{\psi} \gamma^\sigma \psi \right) 
\label{opdef}\end{aligned}$$ where the first three operators are included for checking purposes and all derivatives, both ordinary and covariant, act to the right. In (\[opdef\]) ${\cal S}$ means total symmetrization in the free Lorentz indices and we use the same labelling and notation as [@36] for ease 