Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Choice of dirac matrices

  1. Oct 6, 2011 #1
    Hello!
    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? :/
     
  2. jcsd
  3. Oct 6, 2011 #2

    Bill_K

    User Avatar
    Science Advisor

    There's no reason not to use both. The γ's are useful for relativistic problems, while α, β are useful in the nonrelativistic limit, the relationship being γ0 = β, γi = β αi
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Choice of dirac matrices
  1. Dirac Matrices (Replies: 8)

Loading...