✍ Scribed by Sally Dawson
No coin nor oath required. For personal study only.
I explain the renormalization of the coupling constants, especially sin2 &v , in grand unified theories with complicated gauge hierarchies. The necessary techniques are illustrated in an SU( 16) model.
Recently, a simple formalism has been developed which allows the calculation of the renormalized coupling constants in a unified field theory of the strong, electromagnetic, and weak interactions which has a complicated gauge hierarchy [I]. The method is independent of the details of the symmetry breakdown and so is equally valid in theories with either dynamical or spontaneous symmetry breakdown. In this paper, I review and elaborate on this approach and then I illustrate its use in an SU( 16) model. I consider a theory in which the strong, electromagnetic, and weak interactions are unified in a simple gauge group ~9 at energies above a grand unification mass, M. 99 is broken to W(3) x SU(2) x U(1) in N steps with each stage of the symmetry breakdown occuring at a mass pZ, x = 0 ... N (pN = M). In each stage there is an effective gauge symmetry S", where the generators of Sx are those which are unbroken in stages x through N of the symmetry breakdown: SN = 9, 9 = W(3) x W(2) x U(1): so = W(3) x U(1).
📜 SIMILAR VOLUMES