Related papers: Open associahedra and scattering forms
We clarify the natural cluster algebra of type A that exists in a residual and tropical form in the kinematical space as suggested in 1711.09102 by the use of triangulations, mutations and associahedron on the definition of scattering…
This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. These pertain to a…
Studying the albedos of the planets and moons of the Solar System dates back at least a century. Of particular interest is the relationship between the albedo measured at superior conjunction, known as the ``geometric albedo", and the…
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely…
Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce "stringy canonical forms", which provide a natural…
We report on the analytic computation of the 2-loop amplitude for Bhabha scattering in QED. We study the analytic structure of the amplitude, and reveal its underlying connections to hyperbolic Coxeter groups and arithmetic geometries of…
The "amplituhedron" for tree-level scattering amplitudes in the bi-adjoint $\phi^3$ theory is given by the ABHY associahedron in kinematic space, which has been generalized to give a realization for all finite-type cluster algebra…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
This is a chapter in an upcoming Tamari Festscrift. Permutahedra are a class of convex polytopes arising naturally from the study of finite reflection groups, while generalized associahedra are a class of polytopes indexed by finite…
Tree-level scattering amplitudes of particles have a geometrical description in terms of intersection numbers of pairs of twisted differential forms on the moduli space of Riemann spheres with punctures. We customize a catalog of twisted…
We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory. We do so by introducing and studying…
Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the…
The tree-level scattering amplitudes for $\text{tr}(\phi^3)$ theory can be interpreted as a sum over the vertices of a polytope known as the associahedron. For each graph $G$, there exists a natural generalisation of the associahedron,…
In a remarkable recent work [arXiv : 1711.09102] by Arkani-Hamed et al, the amplituhedron program was extended to the realm of non-supersymmetric scattering amplitudes. In particular it was shown that for tree-level planar diagrams in…
Based on the convex hull construction algorithm, a new geometrical model of ice crystals is proposed to investigate the scattering properties of cirrus clouds particles. Light scattering matrices involving complete polarization information…
This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell's equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
We study two body dipolar scattering in two dimensions with a tilted polarization axis. This tilt reintroduces the anisotropic interaction in a controllable manner. As a function of this polarization angle we present the scattering results…
The geometric structure of S-matrix encapsulated by the "Amplituhedron program" has begun to reveal itself even in non-supersymmetric quantum field theories. Starting with the seminal work of Arkani-Hamed, Bai, He and Yan it is now…
Starting with the unsolved "D\"urer's problem" of edge-unfolding a convex polyhedron to a net, we specialize and generalize (a) the types of cuts permitted, and (b) the polyhedra shapes, to highlight both advances established and which…