Claude Daviau, Jacques Bertrand. Electro-Weak Gauge, Weinberg-Salam Angle, Received 9 October 2015; accepted 20 November 2015; published 23 November 2015, Journal of Modern Physics, 2015, 6, pp. 2080-2092, Published Online November 2015 in SciRes. Free download: http://dx.doi.org/10.4236/jmp.2015.614215
Abstract: The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies sin(θ_W ) = 1/2. We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The U (1)× SU (2) gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.
Keywords: Invariance Group, Dirac Equation, Chirality, Electron, Neutrino, Electro-Weak Gauge, Gauge Bosons, Photon, Weinberg-Salam Angle