abstract

The construction of the conformally flat and inhomogeneous solution of Einstein’s equations is presented. The Bondi type energy tensor has been used as a source.

abstract

It is shown that in the absence of an electric charge, the cosmology arising from the generalised field theory (nonsymmetric theory of electromagnetism and gravitation, GFT) collapses into a static, Einstein universe. The observed expansion is a direct consequence of the presence of a net charge which is shown to be necessarily negative. The implications for GET are discussed.

abstract

We investigate the field equations for Bianchi type-VI\(_0\) space-times with a nonvanishing cosmological constant. Exact solutions are given for the vacuum case of Bertotti–Robinson-type models. In addition a reduction of the field equations to a second order differential equation is given in the general case. The general vacuum case is discussed in various equivalent ways and a transcendental solution is derived.

abstract

We generalize the Królikowski–Rzewuski equation for a distinguished component of the state vector and give the new formulae for a quasipotential and inhomogeneity occurring there. We also study the strong limit (when time goes to infinity) of the quantum evolution operator occurring in this equation. A connection of this limit with the ergodic theorem on the time average is proved.

abstract

After a brief pedagogical reminder of the standard ideas about spontaneous chiral symmetry breaking, we show, after Nambu, how the ideas of B.C.S. theory of superconductivity can be applied to explain dynamically spontaneous chiral symmetry breaking. More specifically, the Bogoliubov–Valatin variational method is applied to a model of massless quarks interacting via a chiral invariant attractive color linear potential. It is shown analytically that due to the quark’s negative self energy, chiral symmetry is spontaneously broken in this model for any value of the parameters.

abstract

The stationary states in proper time quantum mechanics are identified on the basis of physically essential stationarity property. The correspondence with the usual results is established.

abstract

The gauge theory with the gauge group U(\(N \to \infty \)) is solved on a two-dimensional lattice. The single plaquette action used depends on \(L\) parameters, where \(L\) is an arbitrary integer, and thus results for a wide class of variant actions may be compared. A rich structure of second order and third order phase transitions appears. Besides the exact analytic solution a thermodynamical discussion clarifying the qualitative features of the results is given.

abstract

The Kähler equation for differential forms is interpreted in flat space-time as describing a system of two Dirac particles, one of which being infinitely heavy.

abstract

Distribution of the number w of wounded nucleons and of number \(\nu \) of inelastic collisions in \(\alpha \)–\(\alpha \) scattering at high energies is calculated using nuclear probability calculus. Correlatiors between w and v are also studied. The results are compared with generalized optical approximation.

abstract

Exact formula for the statistical distribution function of the fluctuating cross section is presented. Comparison with the results obtained from the approximate formula shows that such a formula can be used for calculation of the cumulative distribution function in the range of its values from 0.01 to 0.99.

abstract

We extend the calculations of a previous paper to include the boundary layer behavior of the solution to the equation \(\varepsilon XYY'=X-Y(Y+1)\). An iteration technique is used to calculate higher-order corrections to the solution.