(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Majorana vector current

Can you offer guidance or do you also need help?

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