Quark-lepton correspondence and the corresponding interpretation of $B-L$ as the fourth color are combined in an $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_R\times {\mathrm{U}}^{\prime }\mathrm{}\left(1\right)\mathrm{}$ electroweak model. The right-handed neutrino interactions are automatically suppressed and the standard model is recovered up to a desirable first-order fine structure. A fundamental distinction is established between the real Weinberg angle and its effective (measured) values. For neutrino interactions, our predictions are in general of the Weinberg-Salam (WS) type, only with the effective replacement ${{sin}^2\theta }_W\to {{sin}^2\theta }_W^{\mathrm{eff}}$ such that (a) ${{sin}^2\theta }_W^{\mathrm{eff}}\left(\mathrm{purely}\mathrm{leptonic}\mathrm{processes}\right)>\mathrm{}{{sin}^2\theta }_W^{\mathrm{eff}}\left(\nu q \mathrm{scattering}\right)$, and (b) for ${{sin}^2\theta }_W=\frac{1}{4}$ one can still have a lower value for the weighted average of ${{sin}^2\theta }_W^{\mathrm{eff}}$. Our expressions for the asymmetry parameter in electron-induced reactions agree with those of the WS model up to a second-order term. The additional neutral gauge boson is expected to be only 1 order of magnitude heavier than $W^{\pm }$. We argue that the present neutral-current experimental data are not capable of distinguishing between the standard and the present models. Finally we discuss the possibility of embedding our model in a unified gauge theory, showing that only spinorial $\mathrm{SO}\mathrm{}(4k+2)\mathrm{}$ theories are available for this purpose.

The idea that fermions acquire their masses via a universal seesaw mechanism can provide a plausible explanation for the mass hier- archy ${\mathrm{m}}_{\mathrm{e}}$,u,d≃${10}^{\mathrm{-}4}$ ${\mathrm{M}}_{\mathrm{W}}$. A minimal SU(3${)}_{\mathrm{C}}$⊗SU(2${)}_{\mathrm{L}}$ ⊗SU(2${)}_{\mathrm{R}}$⊗U(1${)}_{\mathrm{B}\mathrm{-}\mathrm{L}}$ grand unifiable realization is presented. Whereas the fermionic representation is enlarged to include SU(2${)}_{\mathrm{L}}$⊗SU(2${)}_{\mathrm{R}}$ singlets, the Higgs system contains none of the conventional scalars of left-right-symmetric models. An alternative way to account for the superlightness of neutrinos emerges.

A link between (i) the Peccei-Quinn mechanism, (ii) the canonical fermion mass matrix, and (iii) minimal grand unification is established. The effects of a global versus a local horizontal U(1) symmetry are analyzed. It is pointed out that the weak $\mathrm{CP}$ nonconservation in such a model has to be accounted for by Higgs exchanges. A possible bridge to composite models is noted.

As a model, the Pais-Uhlenbeck fourth order oscillator with equation of motion: $(d^{4}q∕d{t}^4)+({\omega }_1^2+{\omega }_2^2)(d^{2}q∕d{t}^2)+{\omega }_1^2{\omega }_2^{2}q=0$ is a quantum-mechanical prototype of a field theory containing both second and fourth order derivative terms. With its dynamical degrees of freedom obeying constraints due to the presence of higher order time derivatives, the model cannot be quantized canonically. We thus quantize it using the method of Dirac constraints to construct the correct quantum-mechanical Hamiltonian for the system, and find that the Hamiltonian diagonalizes in the positive and negative norm states that are characteristic of higher derivative field theories. However, we also find that the oscillator commutation relations become singular in the ${\omega }_1\to {\omega }_2$ limit, a limit which corresponds to a prototype of a pure fourth order theory. Thus the particle content of the ${\omega }_1={\omega }_2$ theory cannot be inferred from that of the ${\omega }_1\ne {\omega }_2$ theory; and in fact in the ${\omega }_1\to {\omega }_2$ limit we find that all of the ${\omega }_1\ne {\omega }_2$ negative norm states move off shell, with the spectrum of asymptotic in and out states of the equal frequency theory being found to be completely devoid of states with either negative energy or negative norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero energy theorem of Boulware, Horowitz, and Strominger, and show how in the equal frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive energy theorem instead.

A horizontal U′(1) gauge symmetry is proposed to distinguish two fermionic generations. By extending the notion of generation structure to the Higgs system, and using anomaly-free conditions with the requirements of lepton-number conservation and proper Cabibbo structure, we determine $Y^{\prime }$ associated with U′(1), uniquely. The model can easily be generalized to account for $2^N$ ($N=1,2,\cdots$) generations.