The Generalised Field Theory GFT: (the nonsymmetric unified field theory of gravitation and electromagnetism with the metric hypothesis) is extended by subjecting it to the action of an U(1) gauge group. It is shown that it then implies a spherically symmetric, static model of an electron with a shell-like structure held by a magnetic force. It is claimed that this prediction represents a possible test of the theory which in principle could be carried out on a laboratory scale.
A new form of phenomenological relativistic \(\gamma \)- law equation of state \[p=k(g_{00})^{-1/2}\varrho ^{\gamma }\] is proposed which seems to be more plausible than the classical one. This equation of state leads to an instructive example of interior Schwarzschild metric, namely the Buchdahl solution. Some numerical deviations from that of classical \(\gamma \)-law equation of state are also given.
Relativistic effects of the order of \(v^2/c^2\) are considered in the wave functions of kaons treated as bound \(q\bar q\)-states. The ratio \(\xi =\left |\frac {\langle r^2_{\rm em}\rangle _{{\rm K}^0}}{\langle r^2_{\rm em}\rangle _{{\rm K}^+}}\right |\) is calculated for dynamical models with the direct interaction. As is shown, in contrast to results by Greenberg, Nussinov and Sucher, corrections to the nonrelativistic \(\xi _{\rm NR}=\frac {m^2_{\rm s}-m^2_{\rm u}}{2m^2_{\rm s}-m^2_{\rm u}}\) may be positive both in the classical and quantum models of \(q\bar q\)-systems.
Data for reaction \(\pi ^-{\rm n} \to {\rm p}\pi ^-\pi ^-\) at 21 GeV/\(c\) are analysed in order to extract information on elastic \(\pi ^-\pi ^-\) scattering. \(\sigma ^{\pi ^-\pi ^-}\) is found to decrease with energy from 5 mb at \(s_{\pi \pi }\simeq 2\) GeV\(^2\) to value below 1 mb for \(s_{\pi \pi }\gt 8\) GeV\(^2\). The data are also compared with predictions of the modified Drell–Hiida–Deck models and reasonable agreement is found.
On the basis of a cluster model we demonstrate the significant difference of the charged multiplicity distributions between annihilation-like (\(\nu p\), \(e^+e^-\) and \(p\bar p\)) and non-annihilation (\(pp\), \(\pi ^+p\) and \(K-p\)) reactions. As for the number distribution of clusters we propose the Gaussian distribution in which a characteristic parameter is chosen according to these unlike reactions, and the asymptotic average numbers of clusters, which lead to KNO scaling, are attributed to the sorts of incident particles. The scaling functions of other reactions are predicted.
A version of the WKB approximation is recalled, which in a simple model of lattice gauge theory is valid at and in the vicinity of the transition point. In this approach the phase transition reflects a singularity in the classical period of the motion considered as a function of the coupling constant.
