abstract

In an earlier work a complex vector algebra for space-time was introduced to provide an abstract alternative to the matrix based tensor-spinor formalisms now in use. By means of the notion of a conjugation, reflections as well as Lorentz rotations in spacetime find simple expression. The investigation of Hermitian and complex symmetric operators provides new insight into the principal correlation between the energy-momentum and Weyl tensors.

abstract

Relations between the geodesic structure, space curvature and such fundamental geometrical objects as metric, connection, Killing vectors, etc. are considered. The consideration is based on exponential mapping and studying of Jacobi’s fields of the first and second orders for which the general solutions are found. The covariant expansions of the fundamental objects in powers of the normal coordinates are constructed in an explicit form, the coefficients being expressed through the curvature tensor and its successive covariant derivatives. The spaces comparison problem is discussed, and the local observables are indicated which are in one-to-one correspondence with the geometry of space provided with to a marked frame.

abstract

Cosmological models with toroidal topology of 3-space in the co-moving frame are obtained as exact solutions of the Einstein equations with sensible energy-stress tensor and the Friedmannian behaviour of the scale factor. The red-shift is found to be isotropic in spite of the model anisotropy.

abstract

The differential and total cross sections of the heavy quark pair production (taking into account the quark anomalous chromomagnetic moment) are presented for electron–nucleon and neutrino-nucleon (at the expense of neutral weak currents) collisions. The contribution of two pole diagrams, describing the interaction of the electron and he neutrino with the gluon from the initial nucleon, is taken into account. The dependence on the quark azimuthal angle and on the virtual boson polarization parameter is studied. Those contributions to the deep-inelastic structure functions which are stimulated by the heavy quark pair creation are calculated in this pole approximation. The influence of the initial photon polarization on the heavy quark pair photoproduction is outlined. It is shown that the available experimental data for the \(J/\varphi \) leptoproduction allows us to obtain the following estimation \(|x|\leq 1.5 \div 2\) (in quark magnetons) for the charm quark anomalous chromomagnetic moment.

abstract

The phenomenological expressions for differential single-particle inclusive cross sections of proton and nucleon production in inelastic p–p and p–n collisions describing the experimental data known at all values of kinematic variables at energies from 5 to several thousand GeV are obtained. Inelasticity coefficients, average multiplicities, kinetic energies and transversal momenta of protons and neutrons are calculated and compared with the experimental data.

abstract

The reaction \(\pi ^-{\rm p} \to {\rm K}^+{\rm K}^-\)n has been studied on a hydrogen target (27000 events) at 18.4 GeV and on a butanol target (54000 events) at 17.2 GeV. In this paper we study the D wave fitting the superposition of f(1270)+A\(_2\)(1310)+f\(^{\prime }\)(1515) resonances to the \(t^4_0\) moment. This fit gives very high \(\chi ^2\)/ND = 60/22 for each sample if the parameters of f\(^{\prime }\)(1515) are fixed at their table values. If these parameters are left free we obtain \(m_{\rm f'} = (1503\pm ^6_7)\) MeV, \({\mit \Gamma }_{\rm f'} = (144\pm ^{19}_{17})\) MeV, and BR(f\('\to \pi \pi /f' \to \) all) = (3.0\(\pm \)1.0)%. Fixing the parameters of f\('\)(1515) to their table values we obtain a good fit after the introduction of a fourth tensor meson with \(m = (1422 \pm 9)\) MeV and \({\mit \Gamma } = (80 \pm 42)\) MeV. Such an object does not easily fit into the quark–antiquark scheme.

abstract

The problem of finding the covariantly constant chromomagnetic field, which minimizes the real part of the energy density, as obtained in the one-loop approximation, is solved for the SU(\(N\)) gauge groups in the \(N \to \infty \) limit.

abstract

Non-linear Klein-Gordon and Dirac equations in 4 dimensions are investigated with the help of a global method based on the use of variable initial conditions. One arrives at very stringent conditions for the existence and non-existence of stable particle-like solutions of several wide classes of non-linear equations. It is shown that for any polynomial non-linearity there exist finite energy solutions with arbitrarily large sizes. On the other hand suitable fractional non-linearities taken alone or added to polynomials satisfy the necessary conditions for having only confined, non-dissipative solutions for any permissible finite value of energy.

abstract

We present some basic properties of the gauge theories in the lattice formulation. We discuss the possible order parameters of the theory and their usefulness from the point of view of the numerical calculations. We study the properties of the low coupling constant expansion, i.e. the continuum limit of the theory. Finally we show the results of the numerical calculations for various lattice systems.

abstract

The concept of the fermion generation charge is introduced. If there arc only familiar intermediate bosons of the first generation, the conservation law of this charge in leptonic processes implies separate conservation laws of the electronic, muonic and tauonic numbers. Otherwise, the former is more general, allowing e.g. for the decay \(\tau ^- \to \mu ^- \mu ^- {\rm e}^+\), though with a diminished rate.