Abstract
The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . 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 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.
Highlights
L. de Broglie found [1] the wave associated to the movement of any particle in 1924
L. de Broglie and his students considered this wave equation as the true wave equation of the electron, not the Schrödinger equation, because it was relativistic; it gave the spin 1/2 property; it gave the true results for the spectroscopy of light
Following de Broglie’s idea, we have previously studied, in Chapter 4 of [23] a way to construct by anti-symmetrical product the quantum wave of a photon from two spinor waves
Summary
L. de Broglie found [1] the wave associated to the movement of any particle in 1924. P. Our article follows the method initiated there This theory of light was not successful at this time, because the photon conserved the mass of the spinor wave, and this mass broke the gauge symmetry. If the quark part is cancelled the wave is reduced to the electron + neutrino case, gauge invariant under the U (1) × SU (2) group of electro-weak interactions. =x′ x′= μσ μ D= ( x) Dνμ x= νσ μ MxM= †; A′ MAM = †; F ′ MFM −1 This is the awaited transformation, because the electromagnetic potential moves with the charges and must be a contravariant space-time vector, while the electromagnetic field of two photons F1 and F2 must transform as each photon field, and this is the case if the electromagnetic field F of a system of two photons is. Searching for anti-symmetrical products with Ψ and its charge conjugate is equivalent to searching anti-symmetrical products with Ψ alone
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