Related papers: The Polynomial Form of the Scattering Equations
We prove that arbitrary (nonpolynomial) scalar evolution equations of order $m\ge 7$, that are integrable in the sense of admitting the canonical conserved densities $\ro^{(1)}$, $\ro^{(2)}$, and $\ro^{(3)}$ introduced in [MSS,1991], are…
Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order, ${\cal O}(G^4)$. As in previous lower-order calculations, we harness powerful tools…
In this paper we study the scattering of non-radial solutions in the energy space to coupled system of nonlinear Schr\"{o}dinger equations with quadratic-type growth interactions in dimension five without the mass-resonance condition. Our…
We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. We obtain infinite linear relations among high energy scattering amplitudes. For some kinematic regimes, we discover that some linear…
We present a novel approximation method that can predict the number of solitons asymptotically appearing under arbitrary rapidly decreasing initial wave packets. The number of solitons can be estimated without integration of the original…
In this paper, we consider the Cauchy problem of Nonlinear Schr\"{o}dinger equation \begin{align*} \left\{\begin{array}{ll}&i u_t+\Delta u=\lambda_1|u|^{p_1}u+\lambda_2|u|^{p_2}u, \quad t\in\mathbb{R}, \quad x\in\mathbb{R}^N…
A method to efficiently compute, in a automatic way, helicity amplitudes for arbitrary scattering processes at leading order in the Standard Model is presented. The scattering amplitude is evaluated recursively through a set of…
Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded…
We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable $S$-matrix theory with…
We derive a set of coupled four-dimensional integral equations for the $NN-\pi NN$ system using our modified version of the Taylor method of classification-of-diagrams. These equations are covariant, obey two and three-body unitarity and…
Scattering methods make it possible to compute the effects of renormalized quantum fluctuations on classical field configurations. As a classic example of a topologically nontrivial classical solution, the Abrikosov-Nielsen-Olesen vortex in…
In addition to the superconformal symmetry of the underlying Lagrangian, the scattering amplitudes in planar N=4 super-Yang-Mills theory exhibit a new, dual superconformal symmetry. We address the question of how powerful these symmetries…
We present the Minkowski space solutions of the inhomogeneous Bethe-Salpeter equation for spinless particles with a ladder kernel. The off-mass shell scattering amplitude is first obtained.
The terms in the quantum scattering in scalar field theory models is parameterized by the invariants $\prod s_{ij}^{n_{ij}}$. The $s_{ij}$ are kinematic two-particle invariants, and the $n_{ij}$ are integers. The coefficients of these terms…
We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.
Soft theorems describe the behavior of scattering amplitudes when one or several external particles are taken to be energetically soft. In tree-level gravity there are universal soft theorems for the three leading orders in the soft…
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\phi^3$-theory. This formalism greatly facilitates the…
We present four examples of integrable partial differential equations (PDEs) of mathematical physics that---when linearized around a stationary soliton---exhibit scattering without reflection at {\it all} energies. Starting from the most…
We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order…
In previous papers [1,2], it was proved that a covariant quantization of the minimally coupled scalar field in de Sitter space is achieved through addition of the negative norm states. This causal approach which eliminates the infrared…