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iangttymn
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With the Lorentz group (SO(1,3) = SU(2)xSU(2)), if you're working with the "true" SU(2) generators N^+_i and N^-_i (rather than the generators J_i and K_i), it is straightforward to find the form of the generators in either spinor rep (0,1/2) or (1/2,0) by setting either N^+ or N^- to zero and setting the other to the Pauli matrices.
Is there an analogous procedure to recover the normal J_i and K_i expressions if you start with (1/2,1/2)? If so, can someone outline how it's done? I'm looking for an explicit derivation of the standard forms of J_i and K_i, using only the fact that we're looking at a (1/2,1/2) representation of SU(2)xSU(2).
Is there an analogous procedure to recover the normal J_i and K_i expressions if you start with (1/2,1/2)? If so, can someone outline how it's done? I'm looking for an explicit derivation of the standard forms of J_i and K_i, using only the fact that we're looking at a (1/2,1/2) representation of SU(2)xSU(2).