Pauli Algebra from Cubic Point-Group Symmetry

Key Points

• The aim is to demonstrate how the Pauli algebra arises from the O_h point-group symmetry of a cubic lattice.
• Utilized standard group theory principles to derive results.
• Examined the T_{1g} subspace of the tensor product T_{1u} ⊗ T_{1u}.
• Showed the connection between symmetry and algebraic structure without assumptions on dynamics.
• Identified three antisymmetric generators in the T_{1g} subspace that satisfy the Lie algebra so(3) ≅ su(2).
• Confirmed that the two-dimensional irreducible representation aligns with the Pauli algebra.
• Established the link between the algebra's structure and the symmetry of the lattice.