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Spin sum

  1. Aug 30, 2008 #1
    Hi,
    there is a good expression for [tex] \sum_{s}{u_s(\vec{p})\bar{v_s}(\vec{p})}[/tex] ?

    Thank you
     
    Last edited: Aug 30, 2008
  2. jcsd
  3. Sep 7, 2008 #2

    Avodyne

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    Not that I know of. But I don't know why you would need this sum; spin sums are needed when a spin is not observed, then you want to sum the absolute square of the transition amplitude over the unobserved spin; but that will always involve u and ubar or v and vbar, but never u and vbar or v and ubar.
     
  4. Sep 8, 2008 #3
    Not always...
    My problem is about Majorana's fermions:

    Take the scattering [tex]\nu_{\tau}+\bar{\nu}_{\tau}\rightarrow \nu_e+\bar{\nu}_e[/tex] and the interaction [tex]{\cal{L}}=g \sum Z_{\mu}\bar{\psi}_{\nu_l}\gamma^{\mu}(1-\gamma_5)\psi_{\nu_l}[/tex].

    The [tex]\nu[/tex] are Majorana's fermions (i.e. [tex]d_r=b_r [/tex]) with mass [tex]m_{\nu_{\tau}}>m_{\nu_e} [/tex]. Compute the cross section. Here the feynman rules are quite difficult and the sums over the spin of the square of the transition amplitude involve also u vbar and v ubar!
    :uhh:
     
  5. Sep 8, 2008 #4

    Avodyne

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    For Majorana fermions, there is always a way to transform things (using spinor identities) so that you get only u ubar or v vbar. This is explained in the book by Srednicki (draft copy available free online, google to find it).
     
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