Related papers: Classical Scattering in $1+1$ Dimensional String T…
These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…
The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…
It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are…
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…
The recently introduced anomaly-free twistor string in 4 dimensions is further explored. The spectrum based on the physical states and its Minkowski interpretation are examined. Scattering amplitudes with vertex operators involving…
In this paper, we consider the Cauchy problem {align*} \{{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 &u(0,x)=\phi(x)\in \Sigma, \quad x\in\mathbb{R}^N, {array}. {align*}…
We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string…
We compute string scattering amplitudes in an orbifold of Minkowski space by a boost, and show how certain divergences in the four point function are associated with graviton exchange near the singularity. These divergences reflect large…
We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is global-in-time and scatters to free waves in…
We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0)…
A systematic way of construction of (1+1)-dimensional dispersionless integrable Hamiltonian systems is presented. The method is based on the classical R-matrix on Poisson algebras of formal Laurent series. Results are illustrated with the…
We describe in detail the techniques needed to compute scattering amplitudes for colored scalars from the infinite tension limit of bosonic string theory, up to two loops. These techniques apply both to cubic and quartic interactions, and…
QCD string is formed at the distances larger than the confinement scale and can be described by the Polchinski--Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion…
We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of…
Using a classical action associated to a point-particle in (1+1)-dimensions the classical string theory is derived. In connection with this result two aspects are clarified: First, the point particle in (1+1)-dimensions is not an ordinary…
String theory provides a compact integral expression for the tree-level scattering amplitude of an arbitrary number of light strings. We focus on amplitudes involving a few tachyons and many photons, with a special choice of polarizations…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant $D$-dimensional tree-level $n$-point amplitudes with pairs of spinning massive particles using compact exponential…
The group theoretic method is extended to include fields with a background charge. This formalism is used to compute the tree level scattering for $W_3$ strings. The scattering amplitudes involve Ising model correlation functions. A…