Regular Series

Vol. 21 (1990), No. 7, pp. 509 – 579

A Mechanism of Compactification

Acta Phys. Pol. B 21, 509 (1990)

page 509 •


A mechanism of compactification is suggested. As it was recently shown by Fukaya some limiting procedures on a subset of Riemannian manifolds are possible. They can lead to physical space-time with almost vanishing cosmological constant in a multidimensional theory. Conditions preventing decompactification are discussed. An example showing that twisted boundary conditions can stabilize the situation is given.

Applicability of Refined Born Approximation to Non-Linear Equations

Acta Phys. Pol. B 21, 513 (1990)

page 513 •


A computational method called “Refined Born Approximation”, formerly applied exclusively to linear problems, is shown to be successfully applicable also to non-linear problems enabling us to compute bifurcations and other irregular solutions which cannot be obtained by the standard perturbation procedures.

A Class of Type D Metrics

Acta Phys. Pol. B 21, 517 (1990)

page 517 •


We study a class of solutions to the Einstein–Maxwell equations that includes the Kinnersley–Walker solutions, but without using a contraction procedure. Type D metric postulated in this paper is endowed with seven arbitrary parameters.

Chaos in Yang–Mills Mechanics

Acta Phys. Pol. B 21, 529 (1990)

page 529 •


Classical Yang–Mills mechanics is studied numerically in detail. Several typical trajectories corresponding to different values of energy were found. The Lyapunov characteristic functions together with the general qualitative analysis suggest that the system for sufficiently big energy exhibits weak chaotic behaviour.

Physics Beyond the Standard Model in the Non-Perturbative Unification Scheme

Acta Phys. Pol. B 21, 541 (1990)

page 541 •


The non-perturbative unification scenario predicts reasonably well the low energy gauge couplings of the standard model. Agreement with the measured low energy couplings is obtained by assuming certain kind of physics beyond the standard model. A number of possibilities for physics beyond the standard model is examined. The best candidates so far are a) the standard model with eight fermionic families and a similar number of Higgs doublets, b) the supersymmetric standard model with five families.

Angular Momentum in Random Walk

Acta Phys. Pol. B 21, 549 (1990)

page 549 •


The influence of the angular momentum on the relationship between nucleon transfer and kinetic energy loss in deep inelastic heavy ion reactions is studied within a discrete two-dimensional random walk formalism. It is found that the dependence upon the number of steps \(q\) of each of the physical quantities calculated is rather insensitive to the angular momentum. When this \(q\)-dependence is converted to energy loss, the sensitivity to \(L\) is increased and becomes more pronounced for larger values of \(E_{\rm Ioss}\) becoming extreme as the energy loss approaches its maximum value for each \(L\), reflecting the fact that in this limit more and more nucleons must be transferred to effect any given increase in the energy loss. On the other hand, this situation is not expected to occur experimentally, where large \(L\)-values are strongly correlated with small energy losses. Thus physical processes at small energy losses, where the sensitivity of the observables to angular momentum is calculably small, are associated with the largest angular momenta, whereas in processes involving larger energy losses where the observed quantities are calculated to have an increasing sensitivity to \(L\), only small angular momenta are involved. Thus the present analysis offers quantitative support for the view that such deep inelastic processes are not very sensitive to the value of the angular momentum. We have also sought to understand the angular momentum dependences calculated as reflecting primarily the angular momentum dependence of the random walk transition probabilities. The results show that the dependence of these probabilities upon \(L\), implicitly through their dependence upon \(E_{\rm Ioss}\), is, for large values of \(E_{\rm Ioss}\), such as to yield qualitatively the calculated dependences upon \(L\) of the several observables.

Viscous Causal Cosmologies

Acta Phys. Pol. B 21, 571 (1990)

page 571 •


We examine a set of spatially homogeneous and isotropic cosmological geometries generated by a class of non-perfect fluids. The irreversibility of this system is studied in the context of causal thermodynamics which provides a useful mechanism to conform to the non-violation of the causal principle.


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