abstract

Regular (static) fluid spheres are those which satisfy certain conditions of differentiability, of positivity of various quantities, and the like. After a review of general conclusions which can be drawn from an appeal to boundary conditions alone the main body of the paper is concerned with a simple regular charged analogue \(S\) of the Schwarzschild interior solution \(S\)*. Any such analogue is here required to share with \(S\)* the property of being conformally flat. Guided by a further property of \(S\)* a second specific assumption then leads to a model with a particularly simple form of \(g_{44}\). This in turn leads to transparent, explicit expressions for various physical quantities of interest. It thus becomes possible to ensure explicitly, without recourse to numerical calculations or to power series, that all conditions of regularity and other conditions arising from physical considerations are satisfied.

abstract

Using a relativistic two-body one-time formalism we derive static potentials which include form-factors for both particles. Another new feature is the derivation of fourth order coupled radial eigenvalue problems taking into account full relativistic angular momentum analysis and spins for both particles. For a particular choice of magnetic form-factors and particular total quantum numbers we demonstrate numerically the existence of high mass electromagnetic resonances.

abstract

An analysis of the interactions of protons and pions at different primary energies (from a few GeV to some thousands of GeV) with emulsion nuclei was made. Experimental data were compared with the predictions of several models, especially of a simple model of non-interacting fireballs (NFB).

abstract

A monopole approximation to the confining potential is proposed. In this approximation spatially separated groups of quarks carry a definite total colour charge. The potentials which lead to the formation of gluon chains are discussed. The generalization of a \((3,\overline {3})\) chain notion, studied by Tiktopoulos, to the case of arbitrary colour charges is given, it is argued that these generalized chains may be unstable with respect to splitting into a system of weakly interacting chains of the \((3,\overline {3})\) type. A unified picture of the high energy hadronic collisions, based on the gluon chain notion and the monopole approximation is proposed. In the meson–meson sector this picture is equivalent to the topological approach. For the other processes it is similar to the approach of Rossi and Veneziano. However, it is argued that the introduction of the junction line into the quark frame is superfluous. The results are expressed in the language of the coloured dual diagrams which provide a generalization of those of Harari and Rosner.

abstract

A new relativistic two-body wave equation is conjectured for a system of one Dirac and one Klein–Gordon particle. The equation is solved exactly for Coulombic bound states in the case of equal, non-zero masses. In particular, a massless stable Coulombic bound state with \(j=1/2\) is shown to exist, provided the coupling constant \(\alpha \) assumes its critical value 2. Such a situation would appear for every unbroken supersymmetric massive pair of one Dirac and one Klein–Gordon particle if only they interacted mutually through a critical Coulombic field.

abstract

Expressions for the Jackson—Feenberg form of the kinetic energy of fermion systems in the chain, hypernetted chain and Percus–Yevick approximations are derived, and critically compared with earlier expressions of this type.

abstract

We discuss thermodynamical quantities related with cosmological event horizons and show that they possess some uncomfortable properties.

abstract

A new approach to lepton and quark spectra, proposed recently, is further developed, in particular for quarks. The existence of elementary black holes of lepton and quark types with spin 1/2 is implied.