Question: Show that the Lorentz group commutation relations (13.20) are satisfied by the choices (K_{i}= pm frac{i}{2} sigma_{i}) and (J_{i}=frac{1}{2} sigma_{i}), where the (sigma_{i}) are Pauli

Show that the Lorentz group commutation relations (13.20) are satisfied by the choices $K_{i}= \pm \frac{i}{2} \sigma_{i}$ and $J_{i}=\frac{1}{2} \sigma_{i}$, where the $\sigma_{i}$ are Pauli matrices.

Data from 13.20

[Ji, Jj] = iijk Jk [Ji, Kj] = iijk Kk [Ki, K;

[Ji, Jj] = iijk Jk [Ji, Kj] = iijk Kk [Ki, K; ]=-iijk Jk,

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