is a vector whose components are the 2×2 identity matrix I 2 for μ μ = 0 and (minus) the Pauli matrices for μ μ ∈ ∈ { 1 , 2 , 3 } . The η η is an arbitrary phase factor, | η η | = 1 , typically taken to be one: η η = 1 . The ω ω is a 2×2 matrix that can be interpreted as the symplectic form for the symplectic group Sp ⁡ ⁡ ( 2 , C ) , which is a double covering of the Lorentz group. It is