We decompose the cosmological redshift in the standard Friedmann cosmologies into two shifts: a Doppler shift attributable to the recession of the galaxies, and a gravitational shift attributable to the curvature of the universe. For galaxies nearby enough for their recessional motion to be non-relativistic, we interpret our results for the Doppler and gravitational shifts with the aid of Birkhoff’s theorem.
In this paper the influence of a prescribed unquantized gravitational field of suitable structure on the system of interacting Maxwell–Dirac fields is investigated on the basis of the \(S\) matrix theory.
The \(S\) matrix constructed in Part I of this work is evaluated for processes which it includes. Some of them are discussed in more detail: pair creation and scattering in an external gravitational field, pair creation by a photon and creation of an electron-positron pair and a photon in an external gravitational field.
Using the dimensional regularization the inclusive cross section for the Coulomb scattering is obtained. It is shown that it gives the same result as the Pauli–Villars regularization. At the end we present some numerical results for the inclusive Coulomb scattering cross-section.
Scattering from a collection of \(N\) fixed non-overlapping scatterers has been considered in a framework which uses as input the corresponding two-body on-shell scattering amplitudes. By introducing a differential operators technique we have been able to reduce the underlying multiple scattering equations to a system of algebraic equations. We exemplify the analysis by discussing a variety of situations for which practical solutions have been known in the literature and show that our method reproduces and generalizes the results obtained by other authors. In particular, our equations are completely equivalent to those obtained in partial wave basis. We turn next to the most interesting high energy scattering case where the partial wave method is impractical and propose two non-eikonal approximation schemes: (i) the never-come-back approximation which neglects reflections and is designed for small angles scattering; and, (ii) the large separation approximation where the relevant expansion parameter is taken to be the ratio of the projectile wavelength to the mutual separation between the scatterers. The latter framework may be regarded as a complementary approach to the former because it includes reflections to all orders and its validity is not restricted to small angles scattering. Furthermore, if the two body amplitude is given in terms of \(l_{\rm max}\) partial waves, the large separation method becomes exact after \((2 l_{\rm max}+ 1)\) iterations.
The cranking method has been treated by means of the Hartree–Fock–Bogolyubov approach and has been applied to the description of fast nuclear rotation in terms of two simple models. The mechanism of the back-bending effect due to a gapless superconductivity, and closely connected with the Stephens–Simon alignment effect, was analysed. The yrast lines turn out to be composed mostly of the HFB vacuum states, however, some of the yrast states are shown to have two quasiparticle character. There is also another mechanism of the back-bending effect possible in our model; it is connected with the disappearance of the superfluid pairing correlations and occurs within the model provided the pairing is strong enough.
An expansion of the Veneziano amplitude for a three-particle decay into two body resonances is studied. It is shown that summing resonances from various channels does not contradict the duality and that the series converges reasonably fast.
