# Expression of $\not{p}$ in Dirac equation

In scattering amplitudes, page 9, equation (2.6), (2.7), $$\not{p}$$ (in the Dirac equation (2.4)) is as follows:

\begin{align} \not{p} = \left( \begin{matrix} 0 & p_{a\dot{b}} \\ p^{\dot{a}b} & 0 \end{matrix} \right), \end{align} where $$p_{a\dot{b}} = \left( \begin{matrix} -p_0+p_3 & p_1-ip_2 \\ p_1+ip_2 & -p_0-p_3 \end{matrix} \right)$$.

But on the other hand, in the article, \begin{align} \not{p} = \left( \begin{matrix} E & \sigma \cdot \vec p \\ -\sigma \cdot \vec p & -E \end{matrix} \right), \end{align} where $$E$$ is the $$2 \times 2$$ identity matrix. Why these two expression of $$\not{p}$$ are different?

In the first reference you are quoting the chiral basis with $$\gamma^0=\begin{pmatrix} 0 & \mathbf{1}_{2\times 2} \\ \mathbf{1}_{2\times 2} & 0 \end{pmatrix}$$ is used while the second reference uses the (standard) Dirac basis $$\gamma^0=\begin{pmatrix} \mathbf{1}_{2\times 2} & 0 \\ 0 & -\mathbf{1}_{2\times 2} \end{pmatrix}$$ see for example the corresponding Wikipedia article.