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I Covariant derivative of field strength tensor

  1. Jan 5, 2017 #1
    Hi,

    I am struggling to derive the relations on the right hand column of eq.(4) in https://arxiv.org/pdf/1008.4884.pdf


    Even the easy abelian one (third row)

    which is

    $$D_\rho B_{\mu\nu}=\partial_\rho B_{\mu\nu}$$

    doesn't match my calculation

    Since

    $$D_\rho B_{\mu\nu}=(\partial_\rho+i g B_\rho)(\partial_\mu B_\nu-\partial_\nu B_\mu)$$

    the equation seems to imply that

    $$B_\rho (\partial_\mu B_\nu-\partial_\nu B_\mu)=0$$

    What am I missing?
     
  2. jcsd
  3. Jan 5, 2017 #2

    Orodruin

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    The field tensor transforms according to the adjoint representation, not the fundamental one. The structure constants for an Abelian group are zero.
     
  4. Jan 5, 2017 #3
    Thank you very much!
     
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