In dimension d = 2, X and Z are the Pauli spin matrices
[[sigma].sub.x] and [[sigma].sub.z].
where the solutions [phi] and [chi] for this electron-vacuum system are 2x1 Dirac spinors, and [??] is the Pauli 2x2 vector matrix derived from the three 2x2 Pauli spin matrices
[[sigma].sub.k](k = 1,2,3) [3, p.12]
where I denotes the 2 X 2 identity matrix and [sigma] are three-vector Pauli spin matrices
In modern usage, biquaternions are classified as one of the Clifford algebras, and are isomorphic to the algebra of (2x2 complex-valued) Pauli spin matrices
. (9-12) Since Maxwell's equations of electrodynamics may be written using such matrices (13), biquaternions may provide a convenient link between electromagnetism and quantum theory.