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Feynman slash notation
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==With four-momentum== This section uses the {{math|(+ β β β)}} [[metric signature]]. 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 gamma matrices, :<math>\gamma^0 = \begin{pmatrix} I & 0 \\ 0 & -I \end{pmatrix},\quad \gamma^i = \begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix} \,</math> as well as the definition of contravariant four-momentum in [[natural units]], :<math> p^\mu = \left(E, p_x, p_y, p_z \right) \,</math> we see explicitly that :<math>\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 & -\vec{\sigma} \cdot \vec{p} \\ \vec{\sigma} \cdot \vec{p} & -E \end{bmatrix}. \end{align}</math> Similar results hold in other bases, such as the [[Weyl basis]].
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