abstract

The role of the Lorentz group in the gauge field theory in the framework of the tetrad theory of gravitation is considered. It is shown that in the tetrad theory covariant with respect to arbitrary tetrad transformations no gauge field is connected with the Lorentz group. A gauge field of the third rank produced by the corresponding Nether invariant the tetrad spin angular-momentum) is introduced by applying the gauge field theory to the group of tetrad Lorentz transformations with constant parameters. It is shown that in the limit of the special relativistic field theory the tetrad spin angular-momentum coincides with the spin angular-momentum of the fermion fields.

abstract

The Friedmann Equation with the bulk viscosity term (coefficient of bulk viscosity = const) is integrated for the dust-filled models. It appears that the introduction of dissipation removes the initial singularity provided it is allowed by the Hawking–Penrose Theorem. Many models obtained by this method, although analytically regular, possess regions with negative energy.

abstract

A formulation of quantum electrodynamics is proposed in which all the propagators and field operators are gauge invariant. It is based on an old idea of Heisenberg and Euler which consists in the introduction of the linear integrals of potentials as arguments of the exponential functions. This method is generalized by an introduction of the so-called “compensating currents”, which ensure local, i.e. in every point of space-time, charge conservation. The linear integral method is a particular case of that proposed in this paper. As the starting point we use quantum electrodynamics with a non-zero, small photon mass (Proca theory). It is shown that, due to the presence of the compensating current, the theory is fully renormalizable in Hilbert space with positive definite scalar product. The problem of the definition of the current operator is also briefly discussed.

abstract

Assuming the Callan-Treiman and Dashen, Li, Pagels, Weinstein relations, exact inequalities for the \(K_{l3}\) scalar form factor \(f(t)\) and its derivatives have been studied. These inequalities are too stringent to fit with the experimental data. Only for a very large value of the propagator \({\mit \Delta }(0)\) of the divergence of the strangeness changing current at zero momentum there is a better agreement. Various causes of this disagreement are analyzed.

abstract

Assuming the geometrical model of particle production, the average multiplicity of negative particles produced in high-energy proton–proton collisions at fixed impact parameter is determined from experimental multiplicity distributions and elastic scattering data. The effects of multiplicity fluctuations and two-component structure at fixed impact parameter are discussed. The results are compared with the predictions of some simple mechanisms of particle production.

abstract

A general formula for coherent scattering on deuterium, including all the complications due to isospin and spin, is derived from Glauber’s theory. The advantage of using tensor transition amplitudes instead of the usual amplitudes with two spin projections as indices is stressed.

abstract

Equilibrium pairing in the deformed rare earth nuclei is calculated by varying energy expression along the trajectory of the constant mean square radius. The Nilsson potential is used in the calculations and its parameters are the only input data for the problem. The resulting equilibrium values of the proton and neutron energy gaps are compared with the values obtained by the standard procedure of fitting the pairing strength to the experimental odd–even mass differences.