abstract

Different anholonomic subspaces of the general relativistic \(\mu \)-space (space of states of a free particle in the gravitational field; i.e. the tangent bundle \(V_8 = T( V_4)\) on the space time \(V_4\)) are introduced which, respectively, represent relativistic analoga of the classical phase space or the space on which the classical theory of radiation defines the distribution function of spectral intensity. These subspaces of \(V_8\) prove to be holonomic, if the 4-velocity field in \(V_4\) the extensions (prolongations) of which are involved in their defining multivector fields is submitted to certain conditions. In this case, from local equations holding for the mapping of sets of points of the subspaces of \(V_8\) and describing the development in time of states of particles, laws of conservation in integral form can be derived.

abstract

Some particular solutions of Einstein’s unified field equations are derived for the electric, cylindrically symmetric case.

abstract

All observable transformations (rotations, Lorentz transformations, and translations) of space-time are assumed to be contained in a de Sitter gauge group. A de Sitter structured connection on a five-dimensional base manifold is considered. The fifth component of the Lorentz gauge potential \(A^{ik}_5\) is interpreted as the electromagnetic field tensor. Requirement of zero torsion gives an interpretation to the fifth coordinate in terms of a length scale factor, as well as the first pair of Maxwell equations in a flat space. A de Sitter gauge invariant Lagrangian reduces to the Langrangian of the Maxwell–Einstein theory on the physical four-dimensional space-time, providing the radius of de Sitter “translations” is small.

abstract

The diffraction of a plane electromagnetic wave by a Schwarzschild black hole is considered. Measurable quantities of the diffraction field (Poynting vector, frequencies) are calculated in the high-frequency approximation for (freely falling) observers very near the horizon. Within two focal regions on opposite sides of the black hole the intensity is strongly amplified but finite, in contrast to the results of geometrical optics. Outside these regions no interference takes place, i.e., geometrical optics holds. According to the different light rays passing through each point of the horizon, there are several images (redshifted or blueshifted) of the radiation source (distant star). The positions and relative intensities of these images are given in terms of the observer’s position at the horizon.

abstract

It is shown that canonical quantization of gravity and matter leads to quantum field theory in curved space-time in the case when the gravitational field can be regarded as a classical background field. The Tomonaga–Schwinger equation for matter in a background field is derived. The physical meaning of momentum constraints of quantum gravity in the presence of matter is established. As an example, the Bianchi type I cosmology is studied and the direction of alteration of evolution caused by created particles is found.

abstract

The multiple scattering model without any corrections due to collective phenomena is shown to describe reasonably well the average numbers of particles produced and interacting nucleons in nucleus–nucleus collisions. Some predictions are given for inclusive spectrum ratios at very high energy.

abstract

We show how the value of the electromagnetic form factor at infinite four-momentum transfer can be estimated using experimental data only over a finite interval of four-momentum transfer and a theorem from the theory of functions.

abstract

A new approach to lepton and quark spectra, proposed recently on the base of difference equations for mass and charge in the discrete space of elementary-fermion generations, is here supplemented by a conjecture about a crucial coefficient. This leads to the predictions \(1788.035\pm 0.004\) MeV and \(28.70604\pm 0.00007\) GeV for the masses of lepton and the next charged lepton, respectively. The predicted mass of toponium \({\rm t}\overline {\rm t}\) is about 36–40 GeV.

abstract

The study of the fragmentation processes in the hadron–hadron interactions is a possible way of investigating a quark–gluon structure of hadrons. In this paper we discuss the fragmentation of mesons and antibaryons into baryons. We have found that these processes are not very well described by different quark models, indicating possibility of an unknown mechanism. We have studied the momentum-charge correlations as a way of measuring the quark charges. The obtained charges are conventional 2/3, \(-1/3\) Gell–Mann–Zweig ones. The study of these correlations has enabled us to determine the average number of the low momentum quark -antiquark pairs, which turns out to be \(\sim 4\).

abstract

Within the framework of general relativistic thermodynamics, the note delivers an account of viscosity and heat conduction in fluids, compatible with wave propagation, via a hidden variable approach. Detailed results are exhibited.