"For its action on spinors, gravity is best described using the spacetime Cliﬀord algebra,
C l(3, 1) — a Lie algebra with a symmetric product. The four orthonormal Cliﬀord vector
γ1 = σ2
⊗ σ1 γ2 = σ2 ⊗ σ2 γ3 = σ2 ⊗ σ3 γ4 = iσ1 ⊗ 1
are written here as (4
× 4) Dirac matrices in a chiral representation, built using the Kronecker
product of Pauli matrices"
I may have to break google with all this looking up of terms :)