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## Homework Statement

Just a matter of convention (question)

## Homework Equations

[tex]\gamma^0 = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 \\0 & 0 & 0 & -1 \end{pmatrix}[/tex]

## The Attempt at a Solution

If then,

[tex]\gamma^0 = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 \\0 & 0 & 0 & -1 \end{pmatrix}[/tex]

and [tex]\gamma^0[/tex] is just [tex]\beta[/tex] and [tex]\beta \alpha^k = \gamma^k[/tex] is it true then that

[tex]\gamma^k = \begin{pmatrix} 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 \\0 & 0 & 0 & -1 \end{pmatrix}\alpha^k[/tex]