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## Main Question or Discussion Point

Hello All,

I'm trying to understand how the (j,j') representation of the Lorentz group. Following Ryder, I can see why we define A=J+iK and B=J-iK, which each form an SU(2) group. So it's clear to me what the rep of these generators is when acting on a state (j,j'): [tex]Rep(A)\otimes1+1\otimes Rep(B)[/tex]. Where Rep(A) and Rep(B) are the appropriate j and j' reps.

My question is this: given the rep [tex](j,j')\oplus(j',j)[/tex], what is the induced rep on the generators? For example how do I act with A or J on this state?

Thanks a whole bunch

I'm trying to understand how the (j,j') representation of the Lorentz group. Following Ryder, I can see why we define A=J+iK and B=J-iK, which each form an SU(2) group. So it's clear to me what the rep of these generators is when acting on a state (j,j'): [tex]Rep(A)\otimes1+1\otimes Rep(B)[/tex]. Where Rep(A) and Rep(B) are the appropriate j and j' reps.

My question is this: given the rep [tex](j,j')\oplus(j',j)[/tex], what is the induced rep on the generators? For example how do I act with A or J on this state?

Thanks a whole bunch