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## Main Question or Discussion Point

This is something I feel I should know by now, but I've always been very confused about. Specifically, how does one determine what each representation of the Lorentz group corresponds to? I mean, I know that the (1/2,0) and the (0,1/2) representations correspond to right and left handed spinors, and the (1/2,1/2) to a 4-vector, but why is that?. I have no idea how to determine this in general. What about the (0,1) and (1,0)? I know they form the electromagnetic tensor, but again I have no clue as to why.

All I can find is something about counting dimensions, or the possible values of j, but that doesn't seem to define things completely... I also found something about determining how those elements transform, but I don't get it. I don't understand what transformations I'm supposed to be looking at.

All I can find is something about counting dimensions, or the possible values of j, but that doesn't seem to define things completely... I also found something about determining how those elements transform, but I don't get it. I don't understand what transformations I'm supposed to be looking at.

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