The problem of finding the energy-momentum tensor in the non-symmetric unified field theory is investigated. It is shown that the definition of such a quasi-tensor due to Einstein and Kaufman leads to the unlikely conclusion that the energy density of matter in the universe vanishes. A tentative solution of this difficulty which gives a non-zero distribution of matter is proposed. The article contains a brief discussion of some unsolved problems of the theory.
A class of exact interior solution for charged spherically symmetric distribution of inhomogeneous matter in an empty background is derived and investigated. It is shown that it is possible for the sphere to expand from a singular state to a maximum proper radius and then collapse again to a singular state. Because there is only one proper reversal in the motion, our model does not exhibit oscillatory motion.
The algebraic classification of the conformal curvature tensor and the energy-momentum tensor on complex space-times are given. These classifications are natural generalizations of the ones well-known in the case of real space times.
The electromagnetic field of a permanently magnetized, rotating sphere without electric charge is calculated up to the first order in the angular velocity with the help of the Maxwell equations in the inertial frame of reference and the previously deduced, generalized Maxwell equations for a non-inertial frame of reference. In this way the field quantities and the charge densities are obtained in both frames of reference directly, i.e. without using transformation formulae for the transition between an inertial frame and a noninertial frame of reference.
One parameter class of post-Newtonian equations of motion is derived from the Einstein field equations. The equations have been obtained in the potential coordinates which are a generalization of the harmonic coordinates.
We find a regular solution of the four-dimensional Euclidean SU(4) Yang–Mills equations. This is the analogue of that of 513(2) found by Belavin, Polyakov, Schwartz and Tyupkin.
It is suggested that the increase of the e/\(\pi \) ratio at low transverse momenta in hadronic collisions is caused by the subprocesses like Q\(\overline {\rm Q} \to {\rm e}^+{\rm e}^-+\)X of quarks and antiquarks created during the space-time evolution of the collision. As a model of such a process we calculate Q\(\overline {\rm Q} \to {\rm e}^+{\rm e}^-+\)“gluon”. The \(p_{\rm T}\) spectra of single leptons and mass spectra of dileptons following from this model are estimated and compared with the data.
The reaction \(\pi ^-\)p \(\to \pi ^-\pi ^-\) + anything was studied at 50 GeV/\(c\) using a multiwire spectrometer of the Dubna–Los Angeles collaboration. We have analysed 497 events at \(m_{\pi \pi } \lt 0.7\) GeV, \(|t| \lt 0.07\) GeV\(^2/c^2\). Using a Chew–Low extrapolation the on-mass-shell cross sections and isospin \(I = 2,\,S\) wave phase shift were obtained. Our results, while consistent with earlier data, yield \(a_0^2 = -(0.20\pm 0.08)\) fm, and seem to disagree with the \(a_0^2 = 0.37 \pm 0.07\) fin obtained from the K\(_{\rm e4}\) decay and the Show and Morgan curve.
Hartree–Fock calculations have been performed for even–even nuclei in the 2p-1f shell. We use the method of Parikh and Svenne considering \(^{40}\)Ca as an inert core. Such calculations are carried out using a velocity dependent effective potential of the s-wave interaction. Binding energies, quadrupole moments, energy gaps and pick up strengths are calculated and compared with the previous results of Parikh and Svenne and with the experimental data, whenever possible. Good agreement is obtained.
