Dirac matrices (${\alpha }_i,\beta$)

Matrices that factor the relativistic energy-momentum relation. In Hamiltonian form, ${\alpha }_i^2={\beta }^2=I$, $\{{\alpha }_i,{\alpha }_j\}=2{\delta }_{ij}I$ and $\{{\alpha }_i,\beta \}=0$. A physical Hamiltonian uses Hermitian matrices; in three spatial dimensions the smallest complex representation has dimension four.