Gauge coupling constants as residues of spacetime representations

Abstract

The gauge coupling constants in the electroweak standard model can be written as mass ratios, e.g. the coupling constant for isospin interactions $g_2^2=2{m_W^2\over m^2}\sim 2({80\over169})^2\sim{1\over 2.3}$ with the mass of the charged weak boson and the mass parameter characterizing the ground state degeneracy. A theory is given which relates the two masses in such a ratio to invariants which characterize the representations of a noncompact nonabelian group with real rank 2. The two noncompact abelian subgroups are operations for time and for a hyperbolicposition space in a model for spacetime, homogeneous under dilation and Lorentz group action. The representations of the spacetime model embed the bound state representations of hyperbolic position space as seen in the nonrelativistic hydrogen atom. Interactions like Coulomb or Yukawa interactions are described by Lie algebra representation coefficients.A quantitative determination of the ratio of the invariants for position and time related operations, determined by the spacetime representation, gives the right order of magnitude for the gauge coupling constants.