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Majorana neutrino mass term

  1. Feb 14, 2010 #1
    In books I find that the Majorana mass term for the neutrinos is given by [tex] m_L \nu_L^T C^\dagger \nu[/tex] where C is Dirac Conjugation operator. How does C look like if I write [tex] \nu_L[/tex] as in terms of its two components [tex]\left(\begin{array} (\nu_{L1} \\ \nu_{L2} \end{array} \right)[/tex]?

    Is [tex] C= (i\sigma^2) =\left(\begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array} \right) [/tex]?

    Thanks for your help!
  2. jcsd
  3. Feb 17, 2010 #2

    Physics Monkey

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    Yes, that looks ok to me. You can read about this in the Dirac chapter of Peskin, there is even a problem about it as I recall.
  4. Feb 21, 2010 #3
    Thanks, the expression is correct. I was confused earlier because when I expand it I get [tex] \nu_1 \nu_2 - \nu_2 \nu_1 [/tex] which I thought is zero. Then it didn't occur to me that the fields are fermionic and they anticommute.
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