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In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the…
We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula is a quantum analogue of the classical inverse scattering transform. It…
Radiative corrections to elastic scattering represent an important part of the interpretation of electron-induced nuclear reactions at small energy transfers, where they make for a dominant part of background. Here we present and validate a…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
We consider both the defocusing and focusing cubic nonlinear Klein--Gordon equations $$ u_{tt} - \Delta u + u \pm u^3 =0 $$ in two space dimensions for real-valued initial data $u(0)\in H^1_x$ and $u_t(0)\in L^2_x$. We show that in the…
Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…
In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $\mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous…
The study of obstacle scattering for the Klein-Gordon equation in the presence of long-range magnetic potentials is addressed. Previous results of the authors are extended to the long-range case and the results the authors previously proved…
Scattering of radial $H^1$ solutions to the 3D focusing cubic nonlinear Schr\"odinger equation below a mass-energy threshold $M[u]E[u] < M[Q]E[Q]$ and satisfying an initial mass-gradient bound $\|u_0\|_{L^2} \|\nabla u_0 \|_{L^2} <…
The duality between partonic and hadronic descriptions of physical phenomena is one of the most remarkable features of strong interaction physics. A classic example of this is in electron-nucleon scattering, in which low-energy cross…
A system of generalized coherent states for the de Sitter group obeying Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar…
Partial wave decomposition is one of the main tools within the modern S-matrix studies. We present a method to compute partial waves for $2\to2$ scattering of spinning particles in arbitrary spacetime dimension. We identify partial waves as…
The non-relativistic scattering of a spin-1/2 particle off a self-dual monopole reduces, for large distances, to the dyon problem, studied previously by D'Hoker and Vinet. The S matrix (calculated by Zwanziger's algebraic method based on…
We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
The scattering of charged solitons in the complex sine-Gordon field theory is investigated. An exact factorizable S-matrix for the theory is proposed when the renormalized coupling constant takes the values $\lambda^{2}_{R}=4\pi/k$ for any…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…