Higgs Fields as Vielbeins of Internal Symmetry Space

Abstract

An earlier suggestion that scalar fields in gauge theory may be introduced as frame vectors or vielbeins in internal symmetry space, and so endowed with geometric significance, is here sharpened and refined. Applied to a $u(1) \times su(2)$ theory this gives exactly the Higgs structure of the standard electroweak theory. Applied to an $su(3)$ theory, it gives a structure having much in common with a phenomenological model previously constructed to explain fermion mixing and mass hierarchy. The difference in physical outcome for the two theories is here traced to the difference in structure between the two symmetry groups.