abstract

The paper discusses certain properties of locally Hermitian and locally Kählerian manifolds. It is shown that a manifold is locally Hermitian if some of its spinorial connection coefficients vanish. Conditions of a similar type are obtained for locally Kählerian manifolds. Subsequently, locally Kähler–Einstein gravitational instantons are investigated. Their vacuum Einstein equations with the cosmological term have been reduced locally to a single non-linear equation of the second order for one real function. This, in turn, has enabled the authors to show that any locally Kähler gravitational instanton with \(R=-4{\mit \Lambda }=\) const. admits locally a real, source-free Maxwell field which for a Kähler gravitational instanton appears to be global. In the latter case, the Einstein–Maxwell equations have been reduced locally to a single differential equation of the fourth order for one real function.

abstract

The “already unified field theory” of the electromagnetic and gravitational fields with a cosmological term on a four-dimensional Riemannian manifold with a positive definite metric is proposed.

abstract

The internal symmetries of relativistic wave equations in the free field case are treated. It is shown that the additional invariance of wave equations is connected with the transformations of physical basis. The dyal symmetry is shown to be the transformation of Lorentz basis.

abstract

Multiplicity distributions from proton-proton interactions are analysed in the framework of two-component model. The asymptotic relations between the dispersion and average multiplicity are discussed using the new data on single proton diffraction at LSR energies. An incompatibility is indicated between the asymptotic stability of relevant phenomenological parameters and the universality of jet parameters for hadron- and lepton–induced processes.

abstract

An exactly solvable quantum mechanical mode] is presented to illustrate the conjecture that leptons and quarks of higher generations may arise as excited states of lepton and quark internal charge distribution kept stable by Poincaré stresses. Excitations are then “quasiphonons” related to internal oscillations around the equilibrium provided by joint action of these stresses and internal electromagnetic forces. The model leads to an exponentially growing mass spectrum proposed previously on the phenomenological ground (predicting toponium at about 40 GeV and the next charged lepton at 28.5 GeV). When perturbed in a natural way, the mode] is able to describe Cabibbo-like mixing of generations, and, in particular, to predict the off-diagonal elements of Kobayashi–Maskawa matrix.