Universality in weak interactions—The cabibbo suppression

An SU₃ gauge model of weak interactions, which generates the Cabibbo suppression spontaneously and consistently, is presented. Out of the eight currents, a triplet couples to relatively light gauge bosons and satisfies the commutation relations of the SU₂-universality algebra of Gell-Mann. The other five couple to necessarily very massive gauge bosons. The leptons have a realistic mass spectrum and the (bare) quarks are massless. The theory as it stands does not encompass charm and cannot suppress strangeness changing neutral currents; both these deficiencies require a larger gauge group for their correction.     

Space inversion of spinors revisited: A possible explanation of chiral behavior in weak interactions

We investigate a model in which spinors are considered as being embedded within the Clifford algebra that operates on them. In Minkowski space M_1,3$M_{1,3}$, we have four independent 4-component spinors, each living in a different minimal left ideal of Cl(1,3)$\mathit{Cl}(1,3)$. We show that under space inversion, a spinor of one left ideal transforms into a spinor of another left ideal. This brings novel insight to the role of chirality in weak interactions. We demonstrate the latter role by considering an action for a generalized spinor field ψαi${\psi }^{\alpha i}$ that has not only a spinor index α but also an extra index i   running over four ideals. The covariant derivative of ψαi${\psi }^{\alpha i}$ contains the generalized spin connection, the extra components of which are interpreted as the SU(2) gauge fields of weak interactions and their generalization. We thus arrive at a system that is left–right symmetric due to the presence of a “parallel sector”, postulated a long time ago, that contains mirror particles coupled to mirror SU(2) gauge fields.     

Purely hadronic weak interactions in unified field theories of the weak and electromagnetic interactions

Non-leptonic weak interactions are investigated in unified gauge theories. A large enhancement of parity violation in nuclei relative to conventional Cabibbo theory is indicated.     

A note on pseudo-Hermitian systems with point interactions and quantum separability

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.     

Difficulties with a unified treatment of nonleptonic weak interactions

The isospin selection rule in a unified treatment ofCP-conserving andCP-violating nonleptonic weak interactions proposed byNishijima andSwank is investigated and compared to that of a modified version.     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

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, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

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The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

On a unified theory of electromagnetism and weak interaction

A unified theory of weak and electromagnetic interaction has been developed on the basis of the assumption that the charge and mass of a lepton is of dynamical origin. According to this model, the spontaneous breakdown of symmetry generates the photon as a Goldstone boson.     

Racemization, chiral stability and weak interactions

We study, in the framework of the Schrödinger's equation, the effect of intermolecular interactions on tunneling racemization of the active molecule. This molecule is assumed as a two-level system and the left-right isomerism is viewed in terms of a double-bottomed harmonic potential well. The active molecule is assumed to be embedded in a gas, liquid or solid, submitted to a perturbing potential U created by the molecules of the sample. In our model we take into account the difference of energy (ε) between the left (L) and right (R) configurations due to the weak interactions. We show that when ε=0 and the perturbing potential U is due to random binary collisions, the optically active system inevitably racemizes. However, when ε≠0 there is chiral stability when ε?δ, where δ is the difference of energy, between left and right configurations, due to the natural tunneling effect. On the other hand, when ε≠0 and U is created by a cooperative effect between the interacting molecules we show that there is no racemization but it is possible to have chiral stability. This occurs when the heterochiral interaction (U_LR) and δ are much smaller than ε. According to our estimates the stability occurs, for typical molecular parameters, only for fundamental harmonic oscillator frequencies , that is, in the infrared and far-infrared regions. In our approach the weak interaction, which is responsible for the left-right symmetry breaking, plays a fundamental role in the optical stability.     

Physical geometry: A unified theory of gravitation,electromagnetism and other interactions

An invariant correlation and a variational principle are given for the theory of connections and frames introduced in previous papers. The relation of the resultant gravitation theory to Yang's theory is clarified. The resultant equations of motion, which imply a generalized Dirac equation, are used to understand geometrically certain aspects of relativistic quantum theory. The conjecture is proposed that electrornegnetism is related to anSU(2) subgroup. The possible association of the extra generators with strong and weak nuclear forces is discussed.     

A gauge theory of weak and electromagnetic interactions with spontaneous parity breaking

We present a unified gauge theory of weak and electromagnetic interactions in which parity is spontaneously broken together with gauge invariance, by the Higgs mechanism. The gauge group is SU(2) × U(1), and a heavy neutrino is associated with every charged lepton. After the breaking of the original parity-conserving theory, both a purely vector electromagnetic current and the usual V-A charged currents are obtained. Z is coupled to a vector electron current, and the model predicts equal $\text{ν}{}_{\mathrm{\mu }}\text{e}\text{and}\text{ν}{}_{\mathrm{\mu }}\text{e}$ cross sections. Extension to hadrons is made by introducing three charmed quarks p′, n′ and λ′ of the same charges as p, n and λ. All the experimental results $\text{(ν}{}_{\mathrm{\mu }}\text{e}\text{,}\text{ν}{}_{\mathrm{\mu }}\text{e}\text{,}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}\text{e}$, ν_μ and $\text{ν}{}_{\mathrm{\mu }}$ hadron scatterings) are compatible with a value of sin²θ_W of order 0.4.     

μ decay and neutrino-neutrino interactions in a non-local theory of weak interactions

The contributions of the ordinary current-current weak interaction and a pure νν interaction to the spectrum of μ decay to second order are analysed in the framework of a non-local theory of weak interactions. Comparison of the obtained results with experimental data allows an upper bound on the coupling constant of the νν interaction to be established.     

Towards a unified gauge theory of gravitational and strong interactions

We study the space-time properties of leptons and hadrons and find it necessary to extend general relativity to the gauge theory based on the four-dimensional affine group. This group translates and deforms the tetrads of the locally Minkowskian space-time. Its conserved currents, momentum, and hypermomentum, act as sources in the two field equations of gravity. A Lagrangian quadratic in torsion and curvature allows for the propagation of two independent gauge fields: translationale-gravity mediated by the tetrad coefficients, and deformational -gravity mediated by the connection coefficients. For macroscopic mattere-gravity coincides with general relativity up to the post-Newtonian approximation of fourth order. For microscopic matter -gravity represents a strong Yang-Mills type interaction. In the linear approximation, for a static source, a confinement potential is found.This essay received an honorable mention (1979) from the Gravity Research Foundation.-Ed.     

Toward a unified field theory of gravitation and strong interactions

The chiralSU(3) quark model is shown to be a consequence of general relativity for Petrov type Id space-times, in much the same way that the Dirac equation is a consequence of special relativity.     

Absolute proton stability in unified models of strong,weak and electromagnetic interactions

We show that the proton can be made absolutely stable, without introducing superheavy bosons, by imposing a global U(1) color symmetry on the Higgs couplings of the theory. Vector-like SU(5) and SU(6) models are discussed in detail.     

A unified theory of quantum holonomies

A periodic change of slow environmental parameters of a quantum system induces quantum holonomy. The phase holonomy is a well-known example. Another is a more exotic kind that exhibits eigenvalue and eigenspace holonomies. We introduce a theoretical formulation that describes the phase and eigenspace holonomies on an equal footing. The key concept of the theory is a gauge connection for an ordered basis, which is conceptually distinct from Mead-Truhlar-Berry’s connection and its Wilczek-Zee extension. A gauge invariant treatment of eigenspace holonomy based on Fujikawa’s formalism is developed. Example of adiabatic quantum holonomy, including the exotic kind with spectral degeneracy, are shown.     

No cross‐interactions between the Weyl graviton and the massless Rarita‐Schwinger field

The proof of the fact that there are no nontrivial, consistent cross‐couplings that can be added between the Weyl graviton and the massless Rarita‐Schwinger field is accomplished by means of a cohomological approach, based on the deformation of the solution to the master equation from the antifield‐Becchi‐Rouet‐Stora‐Tyutin (BRST) formalism. The procedure developed here relies on the assumptions of locality, smoothness, (background) Lorentz invariance, Poincaré invariance, and preservation of the number of derivatives with respect to each field (the last hypothesis was made only in antighost number zero).