- i \tilde{\theta} \epsilon ^{3
0 i} _{\;\;\;\ j} p _{i} \eta ^{j} _{\; \sigma} \mathfrak{g} \left( z , a
\right) \mathfrak{g} \left( a , z ^{\prime} \right) - \tilde{\theta} ^{2} 
p ^{2} \mathfrak{g} \left( z , a \right) \mathfrak{g} \left( a , a
\right) g ^{0} _{\; \sigma} \left( a , z ^{\prime} \right) ,  \label{g0S-2}$$ where we use the result $\epsilon ^{3 0 i} _{\;\;\;\ j} \epsilon ^{3 j
k} _{\;\;\;\ 0} p _{k} p _{i} = p ^{2}$. Solving for $g ^{0} _{\; \sigma} \left( a , z ^{\prime}
\right)$ by setting $z=a$ in Eq. (\[g0S-2\]) and inserting the result back in that equation, we obtain $$g ^{0} _{\; \sigma} \left( z , z ^{\prime} \right) = \eta ^{0} _{\; \sigma} 
\left[ \mathfrak{g} \left( z , z ^{\prime} \right) + \tilde{\theta} p ^{2} \mathfrak{g} \left( a , a \right) A \left( z , z ^{\prime} \right) %
\right] + i \epsilon ^{30i} _{\;\;\;\ \sigma} p _{i} A \left( z , z
^{\prime} \right) ,  \label{g0S-3}$$ where $$A\left( z,z^{\prime }\right) =-\tilde{\theta}\frac{\mathfrak{g}\left(
z,a\right) \mathfrak{g}\left( a,z^{\prime }\right) }{1+ p ^{2} 
\tilde{\theta}^{2}\mathfrak{g}^{2}\left( a,a\right) }.  \label{A(Z,Z)}$$ The remaining components can be obtained by substituting $g ^{0} _{\;
\sigma} \left( a , z 