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Majorana representation of Gamma matrices.

  1. Jul 13, 2008 #1
    It is well known that at times we do need explicit representations for the Dirac gamma matrices while doing calculations with fermions. Recently I found two different expressions for Majorana representation for the gamma matrices. In one paper, the form used is:
    [tex]
    \gamma_{0} = \left(
    \begin{array}{cc}
    0 & i\sigma_2\\
    i\sigma_2 & 0
    \end{array}
    \right)
    [/tex]
    [tex]
    \gamma_{1} = \left(
    \begin{array}{cc}
    \sigma_1 & 0\\
    0 & \sigma_1
    \end{array}
    \right)
    [/tex]
    [tex]
    \gamma_{2} = \left(
    \begin{array}{cc}
    0 & -i\sigma_2\\
    i\sigma_2 & 0
    \end{array}
    \right)
    [/tex]
    [tex]
    \gamma_{3} = \left(
    \begin{array}{cc}
    \sigma_3 & 0\\
    0 & \sigma_3
    \end{array}
    \right)
    [/tex]
    [tex]
    \gamma_{5} = \left(
    \begin{array}{cc}
    \sigma_2 & 0\\
    0 & \sigma_2
    \end{array}
    \right)
    [/tex]
    However in wikipedia article on gamma matrices, the Majorana representations are diffenrent and all are complex matrices. See: http://en.wikipedia.org/wiki/Dirac_matrices#Majorana_basis
    I am confused which is the actual representation of Majorana representation? Or are both representations valid Majorana representations? Note that in the rep. I wrote, the first four matrices are real matrices.

    Also can anybody tell me how to write several matrices side-by-side in latex?
    Thanks.
     
    Last edited: Jul 14, 2008
  2. jcsd
  3. Jul 14, 2008 #2
    Is there any definite rule to obtain gamma matrix representations? Or can I use my own representations if I find the matrices satisfy the anticommutation relations? Is there any limit on the number of possible representations of gamma matrices in a given dimension?
     
  4. Jul 21, 2008 #3

    mjsd

    User Avatar
    Homework Helper

    gamma matrices are only defined up to similarity transformations; which representation or basis you wish to use is up to you.
     
  5. Jul 21, 2008 #4

    Haelfix

    User Avatar
    Science Advisor

    They're also amongst the leading causes of stress disorders amongst physicists.

    The number of times a factor of i, or -1 from a mismatch of conventions with them, has bungled a calculation at this point is a matter of historical importance.
     
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