abstract

It is shown that the set RE of solutions of the Ernst equation can be mapped on a subset \(R^M_{\rm CH}\) of the set of solutions of the Chiral model on the group \(G\) of “unimodular” matrices. The map is a bijection which depends on the choice of a set \(M\) of unimodular matrices; the set plays a role of an external holonomic constraint in the Chiral model. Symmetries of the equations of the Chiral model are investigated. It is shown that (\(2k+ 1\))-soliton solution of this Chiral model generated from \(g_0={\bf 1}\) can be mapped on a solution of the Ernst equation.

abstract

The BRS and BRS transformations are reviewed and applied to the study of unitarity and gauge independence in gauge theories. A geometry of the BRS transformations is introduced through the superfield formalism and the relevance of it to the Adler–Bell–Jackiw anomalies is shown.

abstract

The canonical quantization of the gauge fields and the problems related with gauge invariance are discussed. The elimination of the cyclic variables, to fix the gauge, is worked out in details. The limit of static external charges and the appearance of the parameter \(\theta \) in the quantum theory are considered, and the static stationary points of the euclidean action are introduced.

abstract

The second class current manifestations in the decays \(\tau \to \nu \pi \)V, V \(= \rho , \omega , \varphi \), and \(\tau \to \nu \pi \eta \) are studied. The energy distributions are obtained. The V meson density matrix elements are evaluated. We show that knowledge of these elements allows one to determine all hadron weak current formfactors.

abstract

Spherically symmetric potentials were investigated. It was shown that spherical symmetry excludes nonabelian solutions of Yang–Mills SU(2) equations when certain hypotheses about their sources are supposed.

abstract

An attempt of estimation of the A\(_1\)-meson mass is undertaken. After a short review of the confusing experimental situation, the estimations, based on the SU(3) symmetry, nonrelativistic potential model with the Breit-type Hamiltonian spin structure and Regge pole phenomenology, are discussed. The A\(_1\) mass in vicinity 1200 MeV is favoured.

abstract

A model of relativistically invariant quantum mechanics of spin 0 and spin 1/2 particles is proposed. An invariant evolution parameter is employed, whereas both physical time and the mass of the particle become dynamical quantities. The equations of motion of physical observables are obtained, which correspond to classical formulae.

abstract

Neutron-deficient isotopes of samarium and europium were produced in the \(^{112}\)Sn + \(^{32}\)S (190 MeV) reaction. They were on-line mass separated and studied with the use of Ge X-ray detectors. Three isotopes: \(^{136}\)Sm, \(^{137}\)Eu and \(^{138}\)Eu (with half-lives \(40 \pm 5\) s, \(11 \pm 2\) s and \(12 \pm 2\) s, respectively) were observed for the first time.

abstract

From the optical model analysis of elastic scattering and absorption cross sections of \(\alpha \)-particles including the (\(n,\alpha \)) reaction induced by resonance neutrons it may be concluded that the conception of black nucleus is valid for \(\alpha \)-particles. It was shown that the magnitudes of \(\alpha \)-particle surface spectroscopic factors did not exceed \(10^{-2}\) for all the known \(\alpha \)-transitions both in spherical and deformed heavy nuclei accounting for the ambiguities of the optical model potential. The possibilities of extracting the \(\alpha \)-particle form factors of lowlying nuclear states from \(\alpha \)-transfer reaction data are considered. From all the data considered it is concluded that there is no evidence for the revealing of a-clustering levels in heavy nuclei.