where u is unitary with determinant one, hence in SU(2), and h is Hermitian with trace zero. The trace and determinant conditions imply: h = ( c a − − i b a + i b − − c ) ( a , b , c ) ∈ ∈ R 3 u = ( d + i e f + i g − − f + i g d − − i e ) ( d , e , f , g ) ∈ ∈ R 4 subject to d 2 + e 2 + f 2 + g 2 = 1.