This is the third part of a paper about non-relativistic Schrödinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation ...

In this article we review the construction of local, relativistic quantum vector fields by analytic continuation of Euclidean vector fields obtained as solutions of covariant SPDEs. We revise the formulation of such SPDEs by introducing new Gaussian noise terms – a procedure which avoids the re-definition of the two point functions needed in previous approaches in order to obtain relativistic f...

The phenomenon of scaling in deep inelastic lepton-nucleon scattering is usually explained in terms of the Feynman parton model, and the logarithmic corrections to scaling are explained in the framework of perturbative QCD. For testing the validity of the parton model, we consider the deep inelastic electron scattering in a model in which the system electromagnetic current operator explicitly s...

By using the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation, it is shown that there exists a global mild solution to the Cauchy problem for the relativistic Boltzmann equation with the assumptions of the relativistic scattering cross section including some relativistic hard interactions and the initial data satifying finite mass, “inertia”, energy and entropy.

We discuss the density fluctuations of a fluid due to zero point motion, assuming a linear dispersion relation. We argue that density fluctuations in a fluid can be a useful analog model for better understanding fluctuations in relativistic quantum field theory. We calculate the differential cross section for light scattering by the zero point density fluctuations, and find a result proportiona...

Abstract. A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confine...

We study the inelastic excitations of Xe for electrons with relatively high energies (500 or 750 eV) scattered over large angles, both experimentally and theoretically. In particular, we focus on the shape and intensity of the spectra of inelastically scattered electrons at the sharp dip in the elastic cross section near 135◦ at 750 eV. Under these conditions, the first Born approximation predi...

The existence of soliton solutions is one of the main features of nonlinear wave models solvable by means of the inverse scattering method. Each of these models has associated a particular type of soliton; however, solitons always share a series of common properties: they behave as classical particles and their scattering processes may be interpreted as a succession of paired collisions in whic...

Both the relativistic and non-relativistic model explain very well lowenergy nuclear phenomena, but in a physically different way from each other. There seems to be no low-energy phenomenon to answer which model is more reasonable. In order to explore a difference between two models, high momentum transfer phenomena are investigated. First it is shown that the neutron spin-orbit charge density ...

In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe–Salpeter equation, various quasi–potential equations, the Feynman–Schwinger representation, and similarity transformation methods for Hamiltonian approaches in light–front quantization. Finally, I will comment on ...