abstract

In the near future the experiment will reach a great precision and will be able to test the standard electroweak theory. It is important now to put in order calculations of radiative corrections in this theory and to make correct and exact present theoretical predictions for the measured quantities. The survey of some results of group working in the JINR, Dubna, may serve this aim. We discuss here on-mass-shell renormalization scheme in the unitary gauge; the one-loop amplitudes of both charge and neutral currents-induced fermion scatterings; the large constant effects; the dynamical behaviour of the one-loop neutral-current corrections; the calculation of the \(W\)- and \(Z\)-boson masses; the difference between the various Weinberg parameters \(sin^2 \theta \)w.

abstract

The properties cf the axial-vector current are investigated using dimensional regularization. The modified version of anti-commuting \(\gamma _5\) in \(n\) dimensions is proposed. The VVA and AAA triangle diagrams are precisely calculated. The resulting amplitudes obey the naive vector Ward identifies. In the axial vector Ward identities the Adler–Bell–Jackiw anomalies appear.

abstract

The SVZ method is investigated within a non-relativistic model with the potential \(V = \lambda \) ctg\(^2\) \(\pi x\). Three expansions of the non-relativistic analogon of the exponential moment are considered: the short-time, the weak-coupling and the quasiclassical (in powers of \(\hbar \)) expansions. For potentials which have been studied by now these expansions were indistinguishable. It turns out that the SVZ method applied to the potential \(V = \lambda \) ctg\(^2\) \(\pi x\) works well for small values of the coupling strength \(\lambda \) only if either the short-time or the weak-coupling expansions are used. For large \(\lambda \) only the expansion in powers of \(\hbar \) leads to satisfactory results.

abstract

A relation between the deformation of a single-particle potential of a nucleus and the deformation of the density of matter, generated by this potential, is discussed in detail. Relative difference between the two deformations amounts up to a dozen or so per cent. It is an increasing function of the multipolarity of the deformation. An account of this difference in macroscopic-microscopic calculations of the collective potential energy of a nucleus corrects (increases) its deformation energy.

abstract

An alternative description of the scalar “notivarg” is proposed. The comparison with the original theory of Deser, Siegel and Townsend is given.