abstract

The problem of reducing the new quasirelativistic equation (including radiative corrections to the order \(c^{-3}\) proposed in the previous paper is presented. The well-known iterative Foldy–Wouthuysen method is simplified by introducing an intermediate scheme (generated by the generalized Case transformation) in the investigation of this equation. Supplementing this transformation by two simple unitary transformations, which have only an auxiliary meaning, brings this Hamiltonian to an even form. It is shown that the interpretation of this modified equation is free from difficulties and ambiguities of the Breit equation. All calculations in this paper are restricted to the \(c^{-3}\) term.

abstract

A theorem on obtaining exact solutions for a particular field structure from those of vacuum field equations of general theory as well as from some simpler solutions of unified theories is derived. With the help of this result the most general solution for the particular field structure is developed from the already known simpler solutions. The physical implications of this theorem in relation to some of the parallel work of other authors is discussed.

abstract

It is shown that the generalized mechanics of one masspoint may be interpreted as a special representation of the ordinary mechanics of a system of masspoints. The homomorphism of both representations is shown in the case of two masspoints coupled by a harmonic force. The new representation is applied in the special relativistic mechanics of masspoints.

abstract

The consistency of the three-dimensional Lagrangian formalism in the classical relativistic two-body problem has been considered. Transformation formulae corresponding to the infinitesimal Lorentz transformations have been obtained as a result of a special definition of the connection between coordinate times determining simultaneous positions of two particles in two inertial reference frames. The equation expressing a sufficient form-invariance condition of the equations of motion has been obtained. Conservation laws reflecting the symmetry of the action integral have been found. In particular it has been shown that the centre-of-mass integral is a consequence of the Lorentz-invariance condition. The expression for the centre-of-mass coordinates has been written. The example of a relativistic interaction Lagrangian has been considered. The well-known non-relativistic and quasi-relativistic results can be obtained by means of expansion in powers of \(c^{-2}\).

abstract

An approximative method consisting in combining the procedure of iteration with the best fit of a free parameter is discussed. This method is shown to be particularly simple and exact in a wide range of values of the coupling constant. It deserves to be called a “Refined Born Approximation”. The problem of transition from the case of scattering on an external potential to the case of a mutual scattering of two particles is discussed anew.

abstract

Quantum electrodynamics with compensating current, described in previous publications is further investigated. This paper is devoted to the problem of the definition of the vertex function in this theory. The main difficulty is contained in the fact that the gauge independent and compensating current dependent photon propagator is, in fact, a projector and therefore its inversion does not exist. Thus, the external photon line in the three-point fermion-fermion-photon propagator cannot be cut in an unambiguous way. It is shown, however, that the vertex function can be defined analytically in an unambiguous way by means of the effective external field analogous to the one used in the usual version of the theory. The problem of the renormalization of the gauge-independent vertex function is also considered and it is shown that this quantity obeys the integral equation analogous to one obtained by Brandt with the help of the Wilson expansion. In the Appendices expressions are given for the electron self-energy part and the second integral equation fulfilled by the vertex function.

abstract

We investigate properties of scattering amplitudes that lead to cross sections increasing linearly with energy. A possible application is to neutrino–nucleon scattering.

abstract

A new construction of the quantum field theory is proposed. The general multiplication law for relativistic quantum field theory is discussed. The method is illustrated on the examples of the free field theory and the interacting fields in the so-called one-particle approximation.

abstract

Monte Carlo phase space calculations of the overlap function for Chan–Loskiewicz–Allison and Chew–Pignotti models were performed up to laboratory momentum 1500 GeV. The slope of the overlap function was found to be about four times smaller than the experimental value. Shrinkage of the elastic peak does not exceed the value found in experiment. The qualitative explanation of these results is given and the discrepancy with recent estimates obtained by Hamer and Peierls, Hwa, and Henyey is explained. Finally, it is argued that the random walk picture of the multiperipheral models is not valid foi the realistic pasticle density in the rapidity scale.

abstract

Experimental results on \(\pi ^0\) production in \(K^+\)p interactions at 8.2 GeV/\(c\) incident momentum are presented. Average \(\pi ^0\) multiplicities for given prong numbers are evaluated. They are consistent both with the corresponding results for pp interactions at 12 GeV/\(c\) chosen for comparison because they have the same average prong number) and with a model where total multiplicity distributions are calculated from the Czyżewski–Rybicki formula and the charge branching ratios from the statistical model. Some averages over the \(\pi ^0\) momentum distribution are also evaluated. In particular it is found that \(\pi ^0\)-s produced in two prong interactions go predominantly forward.

abstract

Assuming that in high-energy collisions only pions are produced and that the multi-pion wave function is completely symmetric in all momentum variables, we derive bonds for the different multiplicity-correlations between charged and neutral pions. It is found that in pp and in \(\pi ^{\pm }\)p inelastic scattering the bound for \(f_{c0}\), i.e. , the correlation between charged and neutral pions, is violated by the experimental data. The conclusion is that the wave function cannot be fully symmetric. It is shown that with \(\varrho \)-production, i.e. , with an anti-symmetric wave function, the observed charged-neutral correlation can be explained.

abstract

Production processes of multihadron systems leading to the excitation of the discrete nuclear levels are studied in the framework of the distorted wave impulse approximation model. The influence of the nuclear absorption of the outgoing multiparticle system on the effective mass and momentum transfer distributions is examined. Amplitudes for the process \(\pi ^{12}C\to \pi \pi \pi ^{12}C^*\) (4.4 MeV) are derived and the results compared with experimental data.

abstract

The energies of the quadrupole and hexadecapole vibrational states for some nuclei are calculated in the Actinide region. The influence of the coupling between quadrupole and hexadecapole modes on the vibrational energies is studied.

abstract

The possibility of describing of nuclear levels, alpha-particle and electron scattering experiments within the framework of a unique model is investigated. The nuclear density was generated by single particle potential for electron scattering. For the scattering of alpha-particle on nuclei, the elementary amplitude of alpha-nucleon scattering was used.

abstract

Maxwell equations in the field of a gravitational wave are linearized by means of the weak field approximation. Then the equations are solved in the case of a uniformly magnetized sphere and the dipole electromagnetic radiation power is calculated. These results are applied to compute the electromagnetic radiation emitted by the Earth arid magnetic neutron stars when hit by gravitational radiation.