Scattering amplitudes and integral equations for the collision of two charged composite particles

1980 ◽  
Vol 21 (5) ◽  
pp. 1733-1745 ◽  
Author(s):  
E. O. Alt ◽  
W. Sandhas
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Composite Particles

Multiple scattering of plane harmonic elastic waves in an infinite solid by an arbitrary configuration of obstacles

1969 ◽  
Vol 66 (2) ◽  
pp. 469-480 ◽  
Author(s):  
P. J. Barratt
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Iterative Procedure ◽  
Elastic Solid ◽  
Single Scattering ◽  
Far Field ◽  
Rigid Spheres ◽  
Arbitrary Configuration

AbstractThe multiple scattering of plane harmonic P and S waves in an infinite elastic solid by arbitrary configurations of obstacles is considered. Integral equations relating the far-field multiple scattering amplitudes to the corresponding single scattering functions are obtained and asymptotic solutions are found by an iterative procedure. The scattering of a plane harmonic P wave by two identical rigid spheres is investigated.

On the integral equations for three-body scattering amplitudes

1971 ◽  
Vol 1 (25) ◽  
pp. 1057-1060 ◽  
Author(s):  
V. Vanzani ◽  
G. Cattapan
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Three Body

scholarly journals Scattering Amplitudes, the AdS/CFT Correspondence, Minimal Surfaces, and Integrability

2010 ◽  
Vol 2010 ◽  
pp. 1-31
Author(s):  
Luis F. Alday
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Strong Coupling ◽  
Minimal Surfaces ◽  
Four Dimensions ◽  
Detailed Exposition

We focus on the computation of scattering amplitudes of planar maximally supersymmetric Yang-Mill in four dimensions at strong coupling by means of the AdS/CFT correspondence and explain how the problem boils down to the computation of minimal surfaces in AdS in the first part of this paper. In the second part of this review we explain how integrability allows to give a solution to the problem in terms of a set of integral equations. The intention of the review is to give a pedagogical, rather than very detailed, exposition.

scholarly journals QQ-system and non-linear integral equations for scattering amplitudes at strong coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Davide Fioravanti ◽  
Marco Rossi ◽  
Hongfei Shu
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Bethe Ansatz ◽  
Strong Coupling ◽  
Strong Coupling Limit ◽  
Wilson Loops ◽  
Functional Relations ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

Abstract We provide the two fundamental sets of functional relations which describe the strong coupling limit in AdS3 of scattering amplitudes in $$ \mathcal{N} $$ N = 4 SYM dual to Wilson loops (possibly extended by a non-zero twist l): the basic QQ-system and the derived TQ-system. We use the TQ relations and the knowledge of the main properties of the Q-function (eigenvalue of some Q-operator) to write the Bethe Ansatz equations, viz. a set of (‘complex’) non-linear-integral equations, whose solutions give exact values to the strong coupling amplitudes/Wilson loops. Moreover, they have some advantages with respect to the (‘real’) non-linear-integral equations of Thermodynamic Bethe Ansatz and still reproduce, both analytically and numerically, the findings coming from the latter. In any case, these new functional and integral equations give a larger perspective on the topic also applicable to the realm of $$ \mathcal{N} $$ N = 2 SYM BPS spectra.

Dispersion relations for a two-channel scattering process: residues of the scattering amplitudes

1963 ◽  
Vol 59 (1) ◽  
pp. 161-166
Author(s):  
J. Underhill
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Transfer ◽  
Integral Equations ◽  
Incident Energy ◽  
Dispersion Relations ◽  
Scattering Process ◽  
Image Position

1. This paper is a continuation of a previous one(1), in which dispersion relations satisfied by the scattering amplitudes for a non-relativistic two-channel scattering process were derived. It was shown that for the process described by the integral equationswiththe scattering amplitudes Mi(E, τ) (where E is the incident energy and τ is the momentum transfer), satisfy the relations

scholarly journals The Wilson-loop d log representation for Feynman integrals

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Yichao Tang ◽  
Qinglin Yang
Keyword(s):  
Scattering Amplitudes ◽  
Differential Equations ◽  
Integral Equations ◽  
Wilson Loop ◽  
Boundary Term ◽  
Feynman Integrals ◽  
Four Dimensions ◽  
Loop Integral ◽  
Six Dimensions

Abstract We introduce and study a so-called Wilson-loop d log representation of certain Feynman integrals for scattering amplitudes in $$ \mathcal{N} $$ N = 4 SYM and beyond, which makes their evaluation completely straightforward. Such a representation was motivated by the dual Wilson loop picture, and it can also be derived by partial Feynman parametrization of loop integrals. We first introduce it for the simplest one-loop examples, the chiral pentagon in four dimensions and the three-mass-easy hexagon in six dimensions, which are represented by two- and three-fold d log integrals that are nicely related to each other. For multi-loop examples, we write the L-loop generalized penta-ladders as 2(L − 1)-fold d log integrals of some one-loop integral, so that once the latter is known, the integration can be performed in a systematic way. In particular, we write the eight-point penta-ladder as a 2L-fold d log integral whose symbol can be computed without performing any integration; we also obtain the last entries and the symbol alphabet of these integrals. Similarly we study the symbol of the seven-point double-penta-ladder, which is represented by a 2(L − 1)-fold integral of a hexagon; the latter can be written as a two-fold d log integral plus a boundary term. We comment on the relation of our representation to differential equations and resumming the ladders by solving certain integral equations.

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