abstract

A new invariance property of tensorial functions of the field variables \({\psi }_A\) and their derivatives is presented. This invariance arises from the possibility of replacing the partial derivatives of \({\psi }_A\) by covariant derivatives with respect to a symmetric second order tensor \(\gamma _{\mu \nu }\) possessing properties similar to that of a flat space-time metric tensor. The resulting identities and conservation laws are then discussed. As an example the theory is applied to the Ricci scalar curvature invariant in General Relativity and the resulting conservation law turns out to be the Rosen–Papapetrou identity. In the final section the new method is compared with the more usual Noether method and the differences are given interpretation.

abstract

The residual two-body interaction is investigated. A new term is added to the standard pairing force and its influence on the single particle excitation spectra in heavy nuclei (transuranic region) is examined with special attention given to the behaviour of the so-called “energy gap”, a typical parameter in spectra of even–even nuclei.

abstract

A new method for the derivation of the lower bound for the elastic-to-total cross-section ratio at high energies is presented. It is shown that the constant factor can be improved down to the latest value of the constant in the Froissart bound: e.g. for processes like elastic scattering of \(\pi N\), \(\pi \pi \) etc. one has: \[\sigma _{\rm el}/\sigma _{\rm tot}\geq \frac {m^2_{\pi }\sigma _{\rm tot}}{\pi }\cdot \frac {1}{(\ln s/c\, \sigma _{\rm tot})^2}.\]

abstract

The generalized Lee model with additional nonlocal four-leg \(N{\mit \Theta }\)–\(N{\mit \Theta }\) vertex is studied. The lowest sector is solved for arbitrary choice of the cut-off functions in both vertices. A complete discussion of the \(Z_1=Z_V=0\) limit, defining the composite \(V\)-particle, is presented.

abstract

By using the Goldstone’s theorem, a Universal Regulator is discovered, i.e. the cosmic field being the Yang Mills field of the local scale transformations of space-time coordinates. Its physical role is as follows. Cosmon, the quantum of cosmic field, is a vanishing rest mass, spinless and neutral particle. It is a Universal particle in the sense that it participates in all the physical processes, carrying the interactions in the a causal region \(G_l\) and moreover, if its presence is taken into account, then interactions become microcausal and the theory is free of all the ultraviolet infinities.

abstract

A nonlocal theory of scalar fields is considered, in this theory, by using generalized analytic functions the ultraviolet divergences are eliminated without any regularization. \(S\)-matrix satisfying the unitary and macrocausality conditions is constructed.

abstract

An analysis was carried out of the elastic scattering of 25 MeV alpha particles measured for 24 elements. Experimental angular distributions were reproduced by the Frahn–Venter models, Springer–Harvey models, and the optical model. The models were compared and the angular range applicable for each model and the reproducibility of the \(\sigma _R\) values were examined. For the Springer–Harvey models ambiguity was found, and sets of parameters without physical significance were noted. The geometrical parameters of nuclei were calculated, and the energy dependence of parameters was observed.

abstract

A method of estimating the physical bounds for the linear combinations of components of statistical tensors is presented. Numerical values of the hounds for tensor combinations appearing in the additive quark model predictions for resonance production in two-body processes are calculated.

abstract

A theoretical estimate of the strength and deformation dependence of the two-body interaction producing the nuclear field is discussed and tested by a RPA calculation. The deformation dependent two-body interaction is used to describe the nonaxial quadrupole vibrational state for the large values of the quadrupole deformation of nuclei.

abstract

A method is given of calculating unitary weights in the statistical theory of multiple particle production. This method is considerably simpler than those given in literature.

abstract

Starting with an arbitrary axialsymmetric stationary solution of Einstein equations describing the exterior field of an isolated uncharged source we construct a corresponding class of such solutions of the projective field theory. Outside a finite region the regularity conditions on the axis of symmetry are satisfied. The method is applied to Kerr metric. In this paper electromagnetic fields are not investigated.