The structure constants of are

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Invariance, Ch Lie groups and Lie algebras: rotations, SU(2) and the double cover

Problem

The structure constants of so(3)\mathfrak{so}(3) are fabc=ϵabcf_{abc} = \epsilon_{abc}, giving the adjoint matrices (adJa)bc=−iϵabc(\mathrm{ad}_{J_a})_{bc} = -\mathrm i\epsilon_{abc}. Write out the 3×33\times3 matrix adJx\mathrm{ad}_{J_x} (taking xx as axis 11) explicitly.

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