Electromagnetic tensor and restricted Lorentz group

[TrickyDicky]

How exactly is the EM field tensor related to the proper orthochronous Lorentz group?

 

[Matterwave]

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:

$$F_{\mu'\nu'}=\Lambda^\sigma_{~\mu'}\Lambda^\tau_{~\nu'}F_{\sigma\tau}$$

 

[TrickyDicky]

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:

$$F_{\mu'\nu'}=\Lambda^\sigma_{~\mu'}\Lambda^\tau_{~\nu'}F_{\sigma\tau}$$

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?

 

[dextercioby]

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.