  In the standard model, electroweak theory is based on chiral gauge symmetry,
which only contains massless fermions and gauge vectors. So the fundamental
field equations are Weyl equations including gauge vectors. We deduced these
Weyl equations without gauge vector from quadric surface in three dimensional
oriented projective geometry. It showed that Weyl equations were equations of
generating lines in the quadric surface. In other word, the geometric
correspondence of spinor is generating lines of quadric surface in momentum
space. It also showed that two spinors would generate a gauge vector. After
this quadric surface was localized, its off-origin generating line would
correspond to global Weyl equation including gauge vector, from which we
deduced the global and local gauge transformation.
