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Trace as a product of operators

  1. Jul 9, 2012 #1
    I'm confused about index calculation in eq. 8.25, Mandl QFT textbook. Can anyone give me a detailed explanation showing the equality below?

    [itex]X=\frac{1}{2}A_{\delta \alpha}^+(\bf{p'})\Gamma_{\alpha \beta}(\bf{p'})A_{\beta \gamma}^+(\bf{p})\widetilde{\Gamma}_{\gamma\delta}[/itex]

    [itex]=\frac{1}{2}Tr[A^+(\bf{p'})\Gamma A^+(\bf{p})][/itex]

    Please be patient, I'm learning index notation from scratch.

    Thanks.
     
  2. jcsd
  3. Jul 9, 2012 #2

    A. Neumaier

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    2016 Award

    A factor is missing in your second formula. You can get the corrected formula by application of [tex] Tr A = A_{jj}[/tex] and [tex](AB)_{jk}=A_{jl}B_{lk}[/tex].
     
  4. Jul 9, 2012 #3
    O.k. and

    [itex]Tr(XY^T)=\sum_{i,j} X_{i,j}Y_{i,j}[/itex]

    Thank you.
     
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