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Field Strenght tensor in QED

  1. Dec 16, 2008 #1

    malawi_glenn

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    Hi, I was reading earlier today in Peskin about QED field strenght tensor:

    equation 15.15 and 15.16
    [tex] [D_\mu, D_\nu ] \psi= [\partial _\mu , \partial _\nu ] \psi + ([\partial _\mu, A_\nu] - [\partial _\nu, A_\mu]) \psi + [A_\mu,A_\nu] \psi[/tex]


    Where A is the gauge field...

    That part, I have control over.

    Now I know that the first and last commutator is zero (abelian gauge theory and partial derivatives commute), but the middle one is really bothering me!!

    I obtain:

    [tex] (\partial _\mu A_\nu - \partial _{\nu} A_\mu) \psi + (-A_\nu\partial _\mu + A_\mu \partial _\nu) \psi [/tex]

    And that last [itex](-A_\nu\partial _\mu + A_\mu \partial _\nu) \psi [/itex] should be ZERO, so that:

    [tex] F_{\mu \nu} = [D_\mu, D_\nu ] = \partial _\mu A_\nu - \partial _{\nu} A_\mu [/tex]

    BUT I dont know why ...

    Any help or insight would, I would be very thankful of :shy:
     
    Last edited: Dec 16, 2008
  2. jcsd
  3. Dec 16, 2008 #2

    malawi_glenn

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    I found an older thread "Yang Mills field stress tensor" where George Jones gave an excellent answer!

    :-)
     
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