Geometric interpretation of spinor and gauge vector
Abstract
Description
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.
4 Pages, RevTeX4
4 Pages, RevTeX4