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Electromagnetic tensor and restricted Lorentz group

  1. Nov 29, 2014 #1
    How exactly is the EM field tensor related to the proper orthochronous Lorentz group?
     
  2. jcsd
  3. Nov 29, 2014 #2

    Matterwave

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    What do you mean by "related". As a rank 2 tensor, the Faraday tensor transforms under a proper orthochronous Lorentz transformation just like any other rank 2 tensor:

    $$F_{\mu'\nu'}=\Lambda^\sigma_{~\mu'}\Lambda^\tau_{~\nu'}F_{\sigma\tau}$$
     
  4. Nov 29, 2014 #3
    I mean the specific representation of the group, why is it the direct sum of the (1,0) and (0,1) irreps, is it related with the tensor being a 2-form and its parity invariance?
     
  5. Nov 29, 2014 #4

    dextercioby

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    It has to do with the parity invariance. Just like in the Dirac field case, it's the reason why we need the direct sum of elementary irreducible representations.
     
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