- #1

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I'm trying to write an essay on RQM. The problem I have encountered is the diffrent choices of matrices for the dirac equation.

The two choices that I´m mixing up in my equations are:

\begin{eqnarray}

\gamma^0 = \left( \begin{array}{cc}

I & 0 \\

0 & -I \end{array} \right), \quad

&&\gamma^1 = \left( \begin{array}{cc}

0 & \sigma_1 \\

-\sigma_1 & 0 \end{array} \right), \quad

\gamma^2 = \left( \begin{array}{cc}

0 & \sigma_2 \\

-\sigma_2 & 0 \end{array} \right) \\, \quad

&&\gamma^3 = \left( \begin{array}{cc}

0 & \sigma_3 \\

-\sigma_3 & 0 \end{array} \right),

\end{eqnarray}

And

\begin{eqnarray}

\boldsymbol{\alpha} = \left( \begin{array}{cc}

\boldsymbol{0} & \boldsymbol{\sigma_i} \\

\boldsymbol{\sigma_i} & \boldsymbol{0} \end{array} \right), \quad

&&\beta = \left( \begin{array}{cc}

\boldsymbol{1} & \boldsymbol{0} \\

\boldsymbol{0} & -\boldsymbol{1} \end{array} \right),

\label{dirachpaulimatris}

\end{eqnarray}

I clearly need to work with just one of them.

What are the benefits of working with the former respectivly the latter representation? :/