# Pauli Spin Matrices

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The Pauli spin matrices , and are central to the representation of spin-particles in quantum mechanics. Their matrix products are given by =where I is the 2⨯2 identity matrix and , the Levi-Civita permutation symbol. These products lead to the commutation and anticommutation relations = and , respectively. The Pauli matrices transform as a 3-dimensional pseuodovector (axial vector) related to the angular-momentum operators for spin- by . These, in turn, obey the canonical commutation relations .

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Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshots 1, 2: You can derive the commutation relations for the ladder operators and .

Snapshots 3: The Pauli matrices mutually anticommute.

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