Algebra
The algebraic theory of spin is a carbon copy of the Angular momentum in quantum mechanics theory. First of all, spin satisfies the fundamental commutation relation:
- ,
where εlmn is the (antisymmetric) Levi-Civita symbol. This means that it is impossible to know two coordinates of the spin at the same time because of the restriction of the Uncertainty principle.
Next, the eigenvectors of and satisfy:
where are the creation and annihilation (or "raising" and "lowering" or "up" and "down") operators.
Read more about this topic: Spin Quantum Number
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“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)