abstract

A scheme is presented which extends Ernst’s concise unified derivation of the axially symmetric solutions of Einstein’s field equations to the case of the Brans–Dicke Theory. The method is applied to obtain Tomimatsu–Sato type solutions of the Brans–Dicke theory and the analogues of Schwarzschild and Kerr solutions are rediscovered.

abstract

Metric hypothesis in the nonsymmetric unified field theory of Einstein and Straus is discussed from a group theoretical and fiber bundle point of view. Theoretical background of the hypothesis is constructed. It is shown that the “hypothesis” is in fact implied by the concept of Hermitian symmetry on which the nonsymmetric theory is based.

abstract

It is shown that the many-time Fokker-type action integral corresponds to a single-time action with a Lagrangian depending on higher derivatives (in exact theory — up to infinite order). The expressions for such Lagrangians are found and the corresponding equations of motion, forming a set of ordinary differential equations of infinite order are given. The particular cases corresponding to manifestly invariant Fokker-type action, arbitrary tensor interaction and electrodynamics are considered.

abstract

Symmetry properties of the single-time relativistic Lagrangian of an \(N\)-particle-system corresponding to the many-time action of the Fokker-type, which are a function of derivatives of particle coordinates with respect to time up to infinite order, are investigated. The conditions for quasi-invariance for such a Lagrangian, with respect to a representation of an arbitrary group in infinite continuation of configuration space of the system, are discussed. Using these conditions a general expression for the Lagrangian, securing Poincaré covariance of corresponding equations of motion, is found, and the conservation laws related to this covariance are formulated. In the case of tensor interaction, the expansion of conserved quantities in \(c^{-1}\) up to terms of the order \(c^{-4}\) is performed.

abstract

Padé approximants are used to solve the dispersion relations for the pion photoproduction amplitudes. The proposed modification of the [0,1] Padé approximant leads to a satisfactory description of the nonresonant amplitudes. No free parameters are considered in the calculations. Some of the calculated multipole amplitudes are in better agreement with the experimental data than those obtained b z other methods of solving the dispersion relations.

abstract

A new set of relativistic equations for a spin 1/2 fermion-antifermion bound system in the case of instantaneous interaction have been previously considered by the authors (Acta Phys. Pol. B11, 413 (1980), I). In the present work the 16 amplitudes are re-expressed in terms of three scalars and four vectors which satisfy coupled differential equations. Lorentz, parity and charge conjugation invariance are used to reduce these equations to sets of coupled differential equations according to their parity and total angular momentum. A detailed solution of these equations is given and the positronium case is also studied.

abstract

We observe that the external charges in SU(2) gauge theory can be classified accordingly to their Hopf index. The relationship of this topological classification and the winding number classification of gauge transformations is indicated. The Coulomb solution of the Yang–Mills equations with external charges is obtained with the aid of the gauge transformations characterised by a nonzero winding number.

abstract

The schematic model of nuclear matter proposed by Gomes, Walecka and Weisskopf which was generalized to finite temperatures including interacting Fermi particle aspects is extended here to include nuclear matter with neutron excess. We calculated the level density parameter as a function of neutron excess. We also calculated the temperature dependence of the equilibrium Fermi momentum.