\label{spin1/2transition}
{\left\langle N^*(p,s) \right|} j^{\nu}(0) {\left| N(p+q,s') \right\rangle}=& \overline{N^*}^{(s)}(p)\left[\left( \gamma^{\nu}q^2 - \slashed{q} q^{\nu} \right)F^{NN^*}_{1}\!(Q^2) \right. {\nonumber}\\
&\left.-i \sigma^{\nu \alpha} q_{\alpha} F^{NN^*}_{2}\!(Q^2) \right]\gamma_5 N^{(s')}(p+q) \mbox{ ,}\end{aligned}$$ we can write the unwanted contribution to $\Pi^{\mu\nu}$ as $$\begin{aligned}
\label{BadContribution}
T^{\mu\nu}_{(1/2)}=&\frac{\lambda_{N^*}\lambda_{N}}{(m^2_{N^*}-p^2)(m_N^2-(p+q)^2)} (m_{*}\gamma^{\mu}-4p^{\mu})(\slashed{p}-m_{N^*}) \times {\nonumber}\\&
\left[\left( \gamma^{\nu}q^2 - \slashed{q} q^{\nu} \right)F^{NN^*}_{1}(Q^2) -i \sigma^{\nu \alpha} q_{\alpha} F^{NN^*}_{2}(Q^2) \right]\gamma_5 (\slashed{p}+\slashed{q}-m_{N}) \mbox{ .}\end{aligned}$$ In Refs.[@Belyaev:1995ya; @Peters] it has been shown that it is possible to disentangle the contribution to $\Pi^{\mu\nu}$ due to Eq. and Eq. by a specific choice for the Lorentz basis. As our kinematics are different from those in Ref.[@Peters], we cannot use the same basis, however.

Lorentz basis
-------------

The correlator Eq. satisfies two independent constraints, which have to be taken into account when constructing a suitable Lorentz basis:

-   the transversality condition $q_{\nu} \Pi^{\mu \nu}=0$

-   the Rarita-Schwinger condition $\gamma_{\mu} \Pi^{\mu \nu}=0$ .

As the transversality condition is automatically fulfilled by Lorentz structures proportional to $F^{\mu \nu}$ and its derivatives, it is convenient to construct a basis from these structures. This yields $20$ different Lorentz structures and the QED Bianchi Identity eliminates four thereof. The Rarita-Schwinger condition provides four additional constraints reducing the number of independent Lorentz structures to a mere 12: $$\begin{aligned}
 \mathcal{R}_{1}=&\;qp\;\gamma^{\mu}\slashed{e}\slashed{p} 