Electroweak Theory from SP + SU(2) × U(1): The Higgs Density, the Weinberg Angle, and Precision Tests of the W and Z

This volume uses the Scretching–Planck (SP) density–phase formulation to connect quantum mechanics with the gauge structure of weak, electroweak, and strong interactions. For a scalar wavefunction written as \(\psi=\sqrt{P}\,e^{iS/\hbar}\), the density determines the SP quantum potential, and the phase gradient determines the probability current in the absence of a gauge field. For stationary states with zero current, the energy balance reduces locally to \(E=V+Q_{\mathrm{SP}}\) wherever \(P>0\). Stationary states with nonzero current also include a phase-dependent kinetic term [1–3, 12, 46, 47]. Local phase and internal gauge transformations are implemented through covariant derivatives. The \(U(1)\), \(SU(2)\), and \(SU(3)\) gauge connections have one, three, and eight components, respectively. With independently specified gauge kinetic terms, variation of the coupled actions gives Maxwell’s equations in the Abelian case and the self-interacting Yang–Mills equations in the non-Abelian cases. Quantizing the electromagnetic field and its coupling to charged matter gives QED [1–5, 20, 46, 47]. Part I develops the charged weak current, its low-energy Fermi limit, and the role of the \(W\) mass in setting the range of the charged-current interaction. Part II treats \(SU(2)_L\times U(1)_Y\) electroweak mixing, the Higgs doublet, the Weinberg angle, \(W\) and \(Z\) masses and widths, and precision observables from LEP and SLD. Part III covers \(SU(3)\) color factors, asymptotic freedom, the hadronic \(R\) ratio, quarkonium spectra in the SP formulation, and a lattice estimate of the glueball gap.