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We establish semiclassical resolvent estimates for Schrödinger operators with long-range matrix-valued potentials. As an application, we prove a resonance-free domain in trapping situations. These results generalize the well-known results of [4] [N. Burq, Lower bounds for shape resonances widths of long range Schrödinger operators, Amer. J. Math.124(4) (2002) 677–735] in the case of scalar Schrödinger operators. In addition, we give an estimate on the scattering amplitude for Schrödinger operators with compactly supported matrix-valued potentials.

The electric mean squared radii 〈r²〉_E of Λ(1405) are calculated in the chiral unitary model. We describe the Λ(1405) as a dynamically generated resonance fully in the octet meson and octet baryon scattering. We also consider “Λ(1405)” as a bound state of . For the later “Λ(1405),” we obtain negative and larger absolute value of electric mean squared radius than that of ordinary baryons, which implies that Λ(1405) have structure of widely spread K⁻ around p.

The behavior of the hadron scattering amplitude determined by the gravitation interaction of hadron at high energies with impact of the KK-modes in d-brane models of gravity is examined. The possible periodic structure of the scattering amplitude and its dependence from number of the additional dimensions are analyzed. The effects of the gravitational hadron form factors obtained from the hadron generalized parton distributions (GPDs) on the behavior of the interaction potential and the scattering amplitude are also analyzed. It is shown that in most part the periodic structure comes from the approximation of our calculations.

An explicit calculation of the transition amplitude in the one-loop approximation in Krein space quantization, has been presented in this paper. As we know the loop integrals in the Feynman diagrams will be often diverged, so it is needed to introduce a regulator (Renormalization condition). In Ref. 1 the λϕ⁴ theory in Krein space has been considered, it has been proved that the disappearance of the ultraviolet divergence to the one-loop approximation is the direct result of Krein space quantization method. Here it is shown that the transition amplitude in the one-loop approximation in Krein space is finite, and its quantity has been calculated. So the theory is automatically regularized.

Dark energy and dark matter are two of the biggest mysteries of modern cosmology, and our understanding of their fundamental nature is incomplete. Many parametrizations of couplings between the two in the continuity equation have been studied in the literature, and observational data from the growth of perturbations can constrain these parametrizations. Assuming standard general relativity with a simple Yukawa-type coupling between dark energy and dark matter fields in the Lagrangian, we use the Boltzmann equation to analytically express and calculate the interaction kernel $Q$ in the continuity equation and compare it to that of a typical parametrization. We arrive at a comparably very small result, as expected. Since the interaction is a function of the dark matter mass, other observational data sets can be used to constrain the mass. This calculation can be modified to account for other couplings of the dark energy and dark matter fields. This calculation required obtaining a distribution function for dark energy that leads to an equation of state parameter that is negative, which neither Bose–Einstein nor Fermi–Dirac statistics can supply, and this is the main result of this paper. Treating dark energy as a quantum scalar field, we use adiabatic subtraction to obtain a finite analytic approximation for its distribution function that assumes the FLRW metric and nothing more.

In this contribution the tree-level effective actions for gluons and gravitons, as derived from Open and Closed Superstring theories, are reviewed respectively. As known for a long time, at zero order in α′ (the string fundamental constant) the first action is pure Yang-Mills while the second one is pure Einstein-Hilbert. The first Superstring Theory corrections turn up to appear at order in the first case while they appear at in the second one, as known from the three and four-point scattering amplitudes for gluons and gravitons, respectively. Recent work involving the order contributions to the Yang-Mills action is reviewed with some detail, including the authors' present line of research. Also, the uncharted territory of five graviton scattering is commented, looking forward to derive the Superstring Theory corrections to the Einstein-Hilbert action.

The summation of the partial wave series for Coulomb scattering amplitude, f^C(θ) is usually avoided because the series is oscillatorily and divergent. Instead, f^C(θ) is generally obtained by solving the Schrödinger equation in parabolic cylindrical coordinates which is not a general method. Here, we show that a reconstructed series, (1-cos θ)²f^C(θ), is both convergent and analytically summable.

The reduction formulas for Dirac fermions is derived using the exact solutions of free Dirac equation on de Sitter space–time. In the framework of the perturbation theory one studies the Green functions and derives the scattering amplitude in the first orders of perturbation theory.

We propose a step towards a resolution to black hole information paradox by analyzing scattering amplitudes of a complex scalar field around a Schwarzschild black hole. The scattering cross-section reveals much information on the incoming state but exhibits flux loss at the same time. The flux loss should be temporary, and indicate mass growth of the black hole. The black hole should Hawking-radiate subsequently, thereby, compensating for the flux loss. By examining the purity issue, we comment on the possibility that information bleaching may be the key to the paradox.

A polynomial basis for parity-even three-point amplitudes of higher-spin massless fermions and bosons are derived in four-dimensional space–time from first principles. This basis can be used to construct three-point amplitudes of polarizations of any rank. The results are presented using polarization tensors and tensor-spinors, which is convenient when they are applied to Lagrangian construction.

Using the ambitwistor string theory, we study graviton scattering amplitudes in a light-like linear dilaton background of 10-dimensional supergravity. At the tree level, we find that the three-graviton amplitude coincides with the type-II superstring theory, and the four-graviton or more amplitudes differ from the superstring theory but satisfy the scattering equations. Due to a modified momentum conservation law different at each order in genus expansion, a nonzero amplitude is determined solely from the particular order in perturbation theory without further corrections.

The differential cross-sections for elastic ¹²C–¹²C scattering at 2400 and 1449 MeV are calculated on the basis of the multiple diffraction scattering theory and α-cluster model with dispersion. At the energy 2400 MeV the calculations were performed by means of "effective" and "free" α–α amplitudes. It is shown that the results obtained differ significantly.

We present a strong absorption model with an $S$-matrix in a new form of an antisymmetrized Fermi distribution for describing diffraction patterns of neutron–nucleus scattering at intermediate energies. The proposed antisymmetric $S$-matrix has a form close to the conventional one and allows to obtain exact analytical expressions for the damping factor that determines the elastic scattering amplitude and the total cross-sections for interaction, reactions and elastic scattering. The use of an antisymmetrized Fermi function instead of the usual Fermi function in successful strong absorption models basically does not notably affect the calculated nucleon–nucleus elastic scattering differential cross-sections in the intermediate energy region.

It is known that infinitely many linear relations among string scattering amplitudes appear in high energy limit. These linear relations would imply a symmetry structure that is not manifest before taking the high energy limit. Motivated by this observation, we study an effective field theory of massive spin-2 and spin-1 particles, and try to understand what kind of structure reproduces the linear relations among the amplitudes of bosonic open string.

Rayleigh scattering from a spherical object located near a planar rigid boundary at distances smaller than the wavelength is calculated. Low frequency analysis reduces a scattering problem to a sequence of potential problems. An analytical solution based on expansion in spherical solid harmonics and the use of addition theorem is presented. Analytical perturbation approach is validated by comparison with numerical calculations. The velocity of the center of the particle and the scattering amplitude are determined. In the lowest order in wavenumber, the scattering amplitude is expressed in terms of the monopole and dipole components. In contrast to the behavior of a bubble, under the same conditions, dipole oscillations of the particle in the direction normal to the boundary are not excited and the monopole component of the scattering amplitude does not depend on the location of the particle relative to the boundary.

We report on our study of low-lying resonances in ππ and Kπ scattering from lattice QCD. Based on ab-initio multi-hadron spectroscopy and the Lüscher finite-volume method, we have investigated the elastic scattering amplitudes for ππP-wave, KπS-wave and P-wave partial waves. A particular focus of the discussion will be the parametrizaton of the amplitudes with respect to the identification of resonance parameters. The shown results are obtained for two gauge field ensembles at pion masses 317 MeV and 178 MeV.