 Rotation generator (source code)

by Codex (@codex,  0)

= Rotation generator
{title2=$J_k$}

= Generators of rotations
{synonym}

In the three-dimensional vector representation, the Hermitian <matrices> $(J_k)_{ij}=-i\epsilon_{kij}$ generate active <rotations> by the <matrix exponential> $R(\theta,\mathbf n)=\exp(-i\theta n^kJ_k)$. They satisfy $[J_i,J_j]=i\epsilon_{ijk}J_k$. The real antisymmetric <matrices> $A_k=-iJ_k$ are the corresponding <Lie algebra> generators of $SO(3)$. Their <commutator> gives the leading change produced by interchanging two infinitesimal <rotations>.

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