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We derive an effective Hamiltonian of the relativistic quark model. In the limit of zero quark masses, we obtain linear Regge trajectories for mesons. Based on the diquark-antiquark symmetry, we show that the Regge trajectories of baryons and mesons are parallel at high angular moments. We discuss the breaking of the hadronic supersymmetry and obtain a mass relation of mesons and baryons.

We propose a chiral Lagrangian in which the pions and the vector mesons are treated on equal footing. It gives the usual meson physics and a mass relation for the mesons. We introduce a soliton ansatz for the SU(4) Skyrme model which approximates the more realistic covariant theory. Upon quantization, a rich mass spectrum for the soliton is obtained.

An approach to a unified treatment of Yang-Mills and Higgs fields was proposed previously starting from a noncommutative algebra constructed from the algebra of smooth functions on space-time and the algebra of Hermitian matrices. The formalism was further applied to the bosonic sector of the standard electroweak theory. Here, in order to incorporate fermions into this framework in a natural way, we extend the formalism to include supersymmetry. We find, however, that the scenario changes drastically in the presence of supersymmetry and the conclusions are substantially different. When applied to the standard model, this yields the supersymmetrized bosonic sector of the theory, but the inclusion of quarks and leptons requires additional superfields as in the conventional supersymmetric models.

Miyazawa's supersymmetric generalization of the approximateSU 6 symmetry of hadrons, namelyU 6/21, is shown to arise within the frame of the standard theory of quarks interacting through gluons. The supersymmetry is found to hold in the same approximation for whichSU 6 is a good symmetry, provided a diquark structure emerges through an effective string interaction. The spin independence of the confining force of the strong-coupling regime then explains the near parallelism of the leading Regge trajectories for baryons and mesons. Symmetry breaking is due to mass differences of the constituents and spin-dependent forces caused by gluon exchange. TheU 6/21 algebra is also shown to be embedded in a larger octonionic algebra which puts mesons and baryons, exotic mesons, quarks and diquarks in the same multiplet. The experimental evidence for the existence of qq and $$qq\overline {qq} $$ systems is briefly discussed.

It is shown that Miyazawa’sSU(6/21) superalgebra for hadrons can be applied to a bilocal quark-antiquark (q\(\bar q\)) or quark-diquark (q-D) system resulting in multiplets that include thel=1 mesons in the (35+1) representation ofSU(6) and thel=1 baryons (70−), in addition to thel=0 mesons (35−+1−) andl=0 baryons (56+). Alternatively, a nonsimple algebra that brings together the (35−+1−) mesons and 56+ baryons is also proposed. This minimal scheme does not involve the D-\(\bar D\) exotic mesons in the lowest hadronic supermultiplet. In both schemes color is incorporated through the algebra of split octonions.

A universal gauge theory based on E6 is suggested as a model for the unification of strong, electromagnetic and weak interactions. Left and right components of six quarks (3 light, 3 charmed) and nine leptons (including heavy charged and neutral leptons) are fifted into two 27-dimensional representations of E6. Two different assignments are proposed. The Weinberg angle and the R ratio are derived and the stability of the proton is discussed.

Particle assignments in a unified theory proposed previously are re-examined in both topless and standard versions. Spontaneous symmetry breaking via Higgs fields transforming as 27, 78 and 351 is examined and possible distributions of v.e.v.'s are discussed in both cases. The generation of a 351 effective Higgs field in a two-loop diagram that gives mass to the right-handed neutrino fields is shown to be compatible with the standard model.

A quark model with a core that was previously suggested is used to define a trilocal field to describe mesons. The field is taken to satisfy a second-order equation which is Lorentz invariant and invariant under the linear group acting on the two internal co-ordinates. The local fields occurring in the expansion of the trilocal field then describe mesons with spinJ and multiplicityJ on the leadingρ-A2 linear trajectory. This result shows that such a scheme can accommodate the doubling of the A2-meson and predicts tripling for the R-meson.

A nonlinear realization ofSU3×SU3 for the pseudoscalar mesons is constructed. First, theSU3×SU3 symmetry is broken, while keepingSU2×SU2 exact, by letting the K and η mesons acquire a mass. This model provides a generalization of K-π effective Lagrangians consistent with the Callan-Treiman relations. The symmetry is further broken toSU2×U1 by allowing the pion to have a mass. This is achieved through a one-parameter unitary transformation which has a structure similar to a generalized Cabibbo rotation. This « mass rotation » introduces a part which transforms as the « 27 » representation into the symmetry-breaking term. This term breaks the Gell-Mann-Okubo mode ofSU3 violation and leads to an alternative, accurate mass formula. Divergences of the currents are calculated in both broken-symmetry schemes.

We propose an alternative arising naturally in a six-quark model to the Glashow--Iliopoulos--Maiani mechanism for the suppression of $delta$S = 1 neutral currents. While violating the Cabibbo form of universality, it maintains the tan$sup 2$ theta/sub C/ suppression of strange particle decays and introduces an additional tan theta/sub C/ suppression of charmed-particle decays. (AIP)

We give a fermionic realization of the SU(2) × SU(2) algebra of the Skyrme model. We imbed the SU(2) × SU(2) algebra into U(4) by introducing new generators which are simple modifications of the SU(2) × SU(2) generators. Employing fermionic quantization, we further extend the algebra to a superalgebra. A possible hadronic supersymmetry in the Skyrme model is also discussed.

A connection between strangeness and parity is conjectured in such a way that predictions become possible on the relative parities of strongly interacting particles. (W.D.M.)

The two possible ways of using the exceptional group E6 as a grand unified gauge model are discussed. Natural directions that occur in its breaking are exhibited through a generalization of a method employed by Michel and Radicati. The corresponding Higgs sector is analyzed both for elementary or composite Higgs scalars. The possible enlargement of the electroweak group from SU(2)W × u(l) to SU(2)W × SU’(2)W × u(l) is discussed in the two generations (topless) mode. The possibilities of neutron oscillations and neutrino masses are indicated in both topless and standard (t-quark containing) versions.

The use of E groups for GUTs is discussed. (AIP)The use of E groups for GUTs is discussed. (AIP)