is more important, because representations of SO ⁡ ⁡ ( 1 , 3 ) are not able to describe fields with spin 1/2; i.e. fermions. Here SL ⁡ ⁡ ( 2 , C ) is the group of complex 2 × × 2 matrices with unit determinant, isomorphic to the Lorentz-signature spin group Spin ⁡ ⁡ ( 1 , 3 ) .