Duality Theory of Weak Interactions

The main objectives of this article are 1) to derive a field theory of weak interactions, 2) to study the duality of weak interactions, and 3) to derive the long overdue weak potential and force formula. The new field equations for weak interactions is derived by applying the principle of interaction dynamics (PID) and the principle of representation invariance (PRI) to a standard SU(2) gauge action coupled with the action for the Dirac spinors. The new field equations establish a natural duality between weak gauge fields {Wa μ}, representing the W± and Z intermediate vector bosons, and three bosonic scalar fields φa, representing the neutral Higgs field H0 as recently discovered by LHC and two charged Higgs H±. With the duality, for the first time, we derive layered weak interaction potentials. These potentials clearly demonstrate many features of weak interactions consistent with observations, such as the short-range nature of weak interactions. Also, PID provides an entirely different way of introducing Higgs fields from first principles, and gives rise to a different spontaneous symmetry breaking mechanism.