Related papers: Scattering Forms, Worldsheet Forms and Amplitudes …
In this talk we introduce the properties of scattering forms on the compactified moduli space of Riemann spheres with $n$ marked points. These differential forms are $\text{PSL}(2,\mathbb{C})$ invariant, their intersection numbers…
The search for a theory of the S-Matrix has revealed surprising geometric structures underlying amplitudes ranging from the worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to kinematic space…
We show that the half-integrands in the CHY representation of tree amplitudes give rise to the definition of differential forms -- the scattering forms -- on the moduli space of a Riemann sphere with $n$ marked points. These differential…
In [1], two of the present authors along with P. Raman attempted to extend the Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper we develop various aspects of this proposal. Using recent…
In this paper we explore and expand the connection between two modern descriptions of scattering amplitudes, the CHY formalism and the framework of positive geometries, facilitated by the scattering equations. For theories in the CHY family…
Recently we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units.{[}C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012){]} We assumed each sub-unit…
The so-called Scattering Equations which govern the kinematics of the scattering of massless particles in arbitrary dimensions have recently been cast into a system of homogeneous polynomials. We study these as affine and projective…
The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations…
We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ${\mathbb{CP}^1}$, to higher-dimensional projective spaces $\mathbb{CP}^{k-1}$. The standard, $k=2$…
We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link…
The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We examine the polynomial form of the scattering equations by means of computational algebraic geometry. The scattering equations are the backbone of the Cachazo-He-Yuan (CHY) representation of the S-matrix. We explain how the Bezoutian…
The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time…
We consider the classical self-dual Yang-Mills equation in 3+1-dimensional Minkowski space. We have found an exact solution, which describes scattering of $n$ plane waves. In order to write the solution in a compact form, it is convenient…
We find $n(n-3)/2$-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for $n$ massless particles are real. On these regions, the…
The way we organise perturbation theory is of fundamental importance both for computing the observables of relevance and for extracting fundamental physics out of them. If on one hand the different ways in which the perturbative observables…
We develop a spinor helicity formalism for five-dimensional scattering amplitudes of any mass and spin configuration. While five-dimensional spinor helicity variables have been previously studied in the context of N=2,4 supersymmetric…
We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural…
For a compact manifold with boundary $X$ we introduce the $n$-fold scattering stretched product $X^n_{\text{sc}}$ which is a compact manifold with corners for each $n,$ coinciding with the previously known cases for $n=2,3.$ It is…