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Hermitian conjugate of plane wave spinors for Dirac equation

  1. Oct 28, 2011 #1
    I need to show that

    [itex]u^{+}_{r}(p)u_{s}(p)=\frac{\omega_{p}}{m}\delta_{rs}[/itex]

    where
    [itex]\omega_{p}=\sqrt{\vec{p}^2+m^{2}}[/itex]
    [itex]u_{r}(p)=\frac{\gamma^{\mu}p_{\mu}+m}{\sqrt{2m(m+\omega_{p})}}u_{r}(m{,}\vec{0})[\itex] is the plane-wave spinor for the positive-energy solution of the Dirac equation.

    I think my problem is twofold: I'm not sure I've computed the Hermitian conjugate of the spinor correctly (just the gamma matrix and p have Hermitian conjugates, is that right?) and I'm not sure how/why the normalization term disappears when squared. Either way, I'm not getting the nice simple answer I should!
     
  2. jcsd
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