Pauli matrix commutator identity

a, b \in R^{3}

, the Pauli matrix multiplication law gives

[a \cdot σ, b \cdot σ] = 2 i (a \times b) \cdot σ .

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Cross-product Lie algebra
Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 43 / 4 / Solution
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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 41 / 1 / Solution
Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 44 / 1 / Solution
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Pauli-coordinate left-invariant vector fields on SU(2)

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