Related papers: Two-point derivative dispersion relations
The representation of the usual integral dispersion relations (IDR) of scattering theory through series of derivatives of the amplitudes is discussed, extended, simplified, and confirmed as mathematical identities. Forms of derivative…
We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical…
Integral and derivative dispersion relations (DR) are considered for the $pp$ and $\bar pp$ forward scattering amplitudes. A new representation for the derivative DR, valid at lower energies than the standard one, is obtained. The data on…
Various forms of derivative dispersion relations, in which the dispersion integral is replaced by a series of derivatives of the imaginary part of a scattering amplitude, are reviewed. Conditions of their validity and practical…
We discuss some formal and fundamental aspects related with the replacement of integral dispersion relations by derivative forms, and their practical uses in high energy elastic hadron scattering, in particular $pp$ and $\bar{p}p$…
It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these…
We discuss some analytical and numerical aspects related to the replacement of integral dispersion relations by derivative relations and also the practical applicability of the derivative approach in the investigation of high-energy elastic…
We study the behavior of energy levels in two dimensions for exotic atoms, i.e., when a long-range attractive potential is supplemented by a short-range interaction, and compare the results with these of the one- and three-dimensional…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
We extend the use of derivative dispersion relations to the study of slopes of the real and imaginary amplitudes in pp and p-pbar elastic scattering. The new relations are tested against the solutions for the amplitudes obtained in the…
Making use of a recursive approach, derivative dispersion relations are generalized for an arbitrary number of subtractions. The results for both cross even and odd amplitudes are theoretically consistent at sufficiently high energies and…
In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron…
In QCD sum rules with external fields, the double dispersion relation is often used to represent the correlation function. In this work, we point out that the double spectral density, when it is determined by successive applications of the…
Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\geq 1$ when the density of states…
We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information on hadron structure constants by connecting information from complementary…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
We derive a local, crossing symmetric dispersion relation (CSDR) for 2-2 scattering amplitudes with a parametric ambiguity motivated by string theory. Various limits of the parameter lead to the fixed-t, fixed-s, and other known CSDRs. We…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex-energy solutions of the Schr\"odinger equation, typically when calculating their inner products. In quantum scattering theory the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…