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R(n,dω) = 1 + i Indθ . |
[Ii, Ij] = i εijk Ik. |
Λ(dθ,dv) = 1 + iJdθ + iKdv |
[Ji, Jj] = i εijk Jk , [Ji, Kj] = i εijk Kk , [Ki, Kj] = -i εijk Kk. |
Λ(dη) = 1 + iAdη + iBdη* |
A = 1/2 (J - iK) , B = 1/2 (J + iK) |
[Ai, Aj] = i εijk Ak , [Bi, Bj] = i εijk Bk , [Ai, Bj] = 0 . |
R(n,θ+dθ) = R(n,dθ)R(n,+dθ) = R(n,dθ)(1 + iIndθ) . |
dR/dθ = iR In |
R(n,dθ) = exp(iInθ) ≡ 1 + iInθ + 1/2! (iInθ)2 + ... |