这是一份leeds利兹大学PHYS5390M01的成功案例

$$
g\left(\lambda^{3} \gamma, \lambda \pi_{A^{\prime}}\right)=\lambda^{-1} g\left(\gamma, \pi_{A^{\prime}}\right) \forall \lambda \in C-{0} .
$$
This enables one to define the spinor field
$$
p^{A} \equiv p^{A A^{\prime} B^{\prime}} \pi_{A^{\prime}} \pi_{B^{\prime}} \quad,
$$
and the patching function
$$
f^{A} \equiv p^{A} g\left(p_{B} \omega^{B}, \pi_{B^{\prime}}\right),
$$
and the function
$$
F\left(x^{a}, \pi_{A^{\prime}}\right) \equiv g\left(i p_{A} x^{A C^{\prime}} \pi_{C^{\prime}}, \pi_{A^{\prime}}\right) .
$$

PHYS5390M01 COURSE NOTES ：

and such that
$$
\psi_{A^{\prime} B^{\prime} C^{\prime}}=\mathcal{D}{A A^{\prime}} \gamma{B^{\prime} C^{\prime}}^{A}
$$
The second potential is a spinor field symmetric in its unprimed indices
$$
\rho_{C^{\prime}}^{A B}=\rho_{C^{\prime}}^{(A B)}
$$
subject to the equation
$$
\mathcal{D}^{C C^{\prime}} \rho_{C^{\prime}}^{A B}=0
$$
and it yields the $\gamma_{B^{\prime} C^{\prime}}^{A}$ ‘ potential by means of
$$
\gamma_{B^{\prime} C^{\prime}}^{A}=\mathcal{D}{B B^{\prime}} \rho{C^{\prime}}^{A B}
$$
If we introduce the spinor fields $v_{C^{\prime}}$ and $x^{B}$ obeying the equations
$$
\begin{gathered}
\mathcal{D}^{A C^{\prime}} \nu_{C^{\prime}}=0 \
\mathcal{D}{A C^{\prime}} \chi^{A}=2 i \nu{C^{\prime}}
\end{gathered}
$$