Editing Dirac spinor (section)

===Pauli matrices===
The [[Pauli matrices]] are
<math display="block">
  \sigma_1 = \begin{bmatrix}
    0 & 1\\
    1 & 0
  \end{bmatrix} \quad \quad
  \sigma_2 = \begin{bmatrix}
    0 & -i \\
    i &  0
  \end{bmatrix} \quad \quad
  \sigma_3 = 
  \begin{bmatrix}
    1 &  0 \\
    0 & -1
  \end{bmatrix}
</math>

Using these, one obtains what is sometimes called the '''Pauli vector''':
<math display="block">\vec{\sigma}\cdot\vec{p} = \sigma_1 p_1 + \sigma_2 p_2 + \sigma_3 p_3 =
  \begin{bmatrix} 
    p_3         & p_1 - i p_2 \\
    p_1 + i p_2 & - p_3
\end{bmatrix}</math>