Related papers: Analytical improvements to the Breit-Wigner isobar…
We study the analytic structure of partial-wave amplitudes derived from u- and t-channel exchange processes. The latter plays a crucial role in dispersion-theory approaches to coupled-channel systems that model final state interactions in…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
A hybrid computational method of plane-wave and cylindrical-wave expansions for distributed Bragg-reflector (DBR) pillars is proposed. The plane-wave expansion is employed to represent the one-dimensional periodic structure of the DBR. The…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary…
Model complexity in amplitude analyses is often a priori under-constrained since the underlying theory permits a large number of possible amplitudes to contribute to most physical processes. The use of an overly complex model results in…
This is a survey paper based on previous results of the author. In the paper, we define and discuss the generalizations of linear partial differential equations to multidimensional variational problems. We consider two examples of such…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
The ``spatial interpretation of compositeness'', presented and discussed in [1,2] in the context of non-relativistic potential scattering, is extended to higher partial waves. A particular set of basis states is used to arrive at a slightly…
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
We investigate, by means of numerical simulations, the qualitative properties of a Boltzmann equation for three species of particles introduced in previous work, capturing some features of epidemic spread.
Even if a `complete set' of experimental observables were measured for the elastic scattering or photo/electroproduction of pseudoscalar mesons, ambiguities would remain in the extracted partial-wave and isospin decomposed amplitudes. As…
Perturbative partial-wave amplitudes diverge in cases with a massless exchanged particle in the $t$-channel. We argue that the divergence is an artifact of perturbation theory and give a prescription for the all-orders correction factor…
Whenever the Breit-Wigner amplitude appears in a calculation,there are many instances (e.g., Fermi's two-level system and the Weisskopf-Wigner approximation) where energy integrations are extended from the scattering spectrum of the…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
We discuss the evaluation of the real part of the elementary amplitudes in the context of a multiple diffraction model for $pp$ elastic scattering earlier developed. The framework is based on the concepts of analyticity and polynomial…
We derive a new integral equation that allows the calculation of the scattering or annihilation amplitude of two particles subjected to two potentials when the corresponding amplitude for one potential only is known. We assume that…
Within general partial-wave mixing, a method for reducing the high dimension of the finite-volume Hamiltonian from Hamiltonian effective field theory is proposed. This method provides a new viewpoint on partial-wave mixing, and a set of…