Feynman Slash Notation - With Four-momentum

With Four-momentum

Often, when using the Dirac equation and solving for cross sections, one finds the slash notation used on four-momentum:

using the Dirac basis for the 's,

as well as the definition of four momentum

We see explicitly that

$\begin{align} p\!\!/ &= \gamma^\mu p_\mu = \gamma^0 p_0 + \gamma^i p_i \\ &= \begin{bmatrix} p_0 & 0 \\ 0 & -p_0 \end{bmatrix} + \begin{bmatrix} 0 & \sigma^i p_i \\ - \sigma^i p_i & 0 \end{bmatrix} \\ &= \begin{bmatrix} E & - \sigma \cdot \vec p \\ \sigma \cdot \vec p & -E \end{bmatrix} \end{align}$

Similar results hold in other bases, such as the Weyl basis.

Read more about this topic: Feynman Slash Notation