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Majorana vector current

  1. Jan 4, 2019 #1
    1. The problem statement, all variables and given/known data
    I am trying to show that Majorana vector current vanishes. I am following this article and I am trying to get to the very right hand side of eq. (27).

    2. Relevant equations
    [tex]\psi_M^C = \psi_M,\\ \psi^C_M = C \overline{\psi}_M^T,\\ C^T=-C, \hspace{1cm} C^T\gamma_{\mu}C = -\gamma_{\mu}^T.[/tex]

    3. The attempt at a solution
    Vector current is
    [tex]\overline{\psi^C}_M \gamma_{\mu} \psi_M^C = C\psi_M^T \gamma_{\mu} C \overline{\psi}_M^T\\
    =-\overline{\psi}_M^T C \gamma_{\mu} C \psi_M^T\\
    =\overline{\psi}_M^T C^T \gamma_{\mu} C \psi_M^T\\
    = -\overline{\psi}_M^T \gamma_{\mu}^T \psi_M^T,
    [/tex]
    where I switched the order of [itex]\psi_M^T[/itex] and [itex]\overline{\psi}_M^T[/itex] from first to second row and then used the last row of relevant equations to the end result.
    Is this correct and enough?
     
  2. jcsd
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