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Difference in sign

  1. Aug 4, 2007 #1
    I have a hard time trying to derive the equation in 6.4 . This is what I've done, and as you will see I have a sign difference compared to his.
    http://scitation.aip.org/getpdf/ser...70000001015012000001&idtype=cvips&prog=normal
    Starting with page 8, equation 6.2, considering the second term in the action, i.e.

    [tex] D_{\mu}\overline{\psi}\gamma^{\mu}\psi[/tex]

    note: the author used the four-component Dirac spinor as [tex]\left(
    \begin{array}{cc}
    \chi\\
    \overline{\psi}
    \end{array}
    \right)
    [/tex]

    I also calculated some identities:
    [tex]\psi* \gamma^0 \gamma^{\mu} = \gamma^0 \gamma^{\mu} \psi* [/tex]
    [tex]\gamma^{\mu}\gamma_{\mu} = 4 [/tex]
    [tex] \{\gamma^{\mu} , \gamma^{\nu}\} = 2g^{\mu\nu} [/tex]

    With these,
    I obtain for [tex] \frac{1}{4z}\gamma_{\mu}\gamma_{5}\overline{\Psi}\gamma^{\mu}\Psi = \frac{-2}{z}(\chi\psi - \overline{\chi}\overline{\psi}) [/tex]

    I have a sign difference with the author's in equation 6.4
    I calculated for the first term too. Still a sign difference. In fact, I get something like [tex]\frac{3}{z} (\chi\psi - \overline{\chi}\overline{\psi})[/tex]
     
    Last edited: Aug 4, 2007
  2. jcsd
  3. Aug 4, 2007 #2

    quasar987

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    you might want to provide the name of the book you're using?
     
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