Speaker
Description
Based on the general principles of Lorentz symmetry and unitarity, we introduce two consistency
conditions – on-shell gauge symmetry and strong massive-massless continuation – in constructing
amplitudes of massive gauge theory with elementary particles. In particular we argue that on-shell
gauge symmetry can be understood as a consequence of Lorentz symmetry, unitarity and massivemassless continuation. Based on these two conditions, combined with the little group transformation
and consistent factorization, we construct 3-point and 4-point vector-boson/scalar amplitudes that
correspond to renormalizable interactions, then analyze the underlying theories and models. Given
the particle masses, almost all possible vertices, including those involving Goldstone modes, are
uniquely fixed. The only exceptions are triple and quartic scalar self-couplings. In addition, all
particle masses must have the same physical origin. If the number of vector bosons is smaller than
3, the underlying theories for the amplitudes are either massive gauge theories with spontaneous
symmetry breaking (S.S.B.) or Stueckelberg theory. The necessary condition for the latter is that the
scalars have equal masses. We also discuss different models depending on the number of scalars
involved. If the number of vector bosons is larger than 3, the underlying theory must be Yang-Mills
theory with S.S.B. In both Abelian and non-Abelian cases, the specific shape of the Higgs potential
cannot be determined, which explains the fact that scalar self-couplings are undetermined, and the
relations between the masses are generally nonlinear.
