Step 1: Recall the Dirac-Pauli representation of the gamma matrices:
In the Dirac-Pauli representation, the gamma matrices are given by:
$$
\gamma^0 = \begin{pmatrix} I & 0 \\ 0 & -I \end{pmatrix}, \quad \gamma^i = \begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0
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