abstract

An approach to the quantization problem of gauge fields, based on the external source method combined with the quantum dynamical equation is presented.

abstract

By using the theory of fiber bundle, the path dependent quantities used by Mandelstam to derive the Feynman rules for the Yang–Mills and gravitational fields are shown to be just the quantities taken on a horizontal path of a fiber space. This geometric meaning enables us to construct new path dependent quantities remaining unchanged under gauge transformations.

abstract

The method of sidewise dispersion relations is used for the calculation of anomalous magnetic moments (a. m. m.) and constants of “weak magnetism” of electromagnetic and weak \(B(J^P=\frac {1}{2} ^+) \to B'(J^P =\frac {1}{2} ^+)\) transitions. The performed analysis shows that the values of a. m. m. of octet baryons calculated with the method mentioned above, and compared with the experimental data and the ratio of “weak magnetism” constants of different weak baryon–baryon transitions do not contradict the predictions of Cabibbo’s model.

abstract

The classical limit of nonrelativistic quantum mechanics in the Wigner phase-space formalism is discussed. It appears that the limit of an eigenstate is represented by a singular probability density concentrated and constant on subsets of phase space corresponding to the given value of the observable. The limit of eigenstates of energy is investigated as an example.

abstract

The standard time-dependent description of the scattering processes is used to explain that, when the \(S\)-matrix does not conserve energy, the coefficient relating the squared modulus of the \(S\)-matrix element to the cross-section becomes model-dependent, and the optical theorem does not necessarily follow from the unitarity of the \(S\)-matrix. It is suggested that, if one insists on using such models, the optical theorem should be imposed as a constraint and used to fix the model-dependent coefficient.

abstract

A new quasipotential two-particle theory is presented for the description of the spinless relativistic hydrogen atom. Recoil effects are fully taken into account, but are shown to have no effect on the fine structure of the spectrum. For an infinitesimal value of the fine-structure constant \(\alpha \) the theory has O(4) symmetry. Apart from the recoil effects the energy levels in this case coincide with those of the Dirac atom with maximum spin value. For a nonvanishing value of \(\alpha \) the O(4) symmetry is broken in the same order in \(\alpha \) in which the Lamb-shift occurs. The Klein paradox probably does not exist.

abstract

The gamma–gamma angular correlations in the decay \(^{153}\)Tb–\(^{153}\)Gd have been studied employing Ge(Li)–Ge(Li) detectors. The \(A_2\) and \(A_4\) coefficients have been determined for the following cascades: 82.9 — 87.6, 82.9 — 19 — 109.7, 82.9 — 129.1, 102.2 — 68.2, 139.7 — 109.7. 174.3 — 87.6, 174.3 — 19 — 109.7, 102.2 — 109.7, 186.9 — 129.1, 193.7 — 109.7, 206.7 — 109.7, 332.5 — 109.7, 835.4 — 109.7, 845.6 — 109.7 and 991.7 — 109.7 keV. The mixing rations of gamma-transitions 68.2, 87.6, 109.7 and 129.1 keV and the spins for 41.5(5/2), 109.7(5/2), 129.1(3/2), 211.9(3/2), 249.5(5/2), 303.5(5/2), 316.1(3/2), 442.5(5/2), 945.1(3/2), 955.3(5/2) and 1101.5(3/2) keV states have been deduced. The possible spin values of other states have been also analysed.

abstract

The results of an analysis of possible helicity states, based on the relativistic quark model, for diffractively produced mesonic systems are reported here. The model explains approximate \(t\)-channel helicity conservation (TCHC) in pion diffractive dissociation.