Related papers: The combinatorial geometry of particle physics
A Green's function formalism to analyze the scattering properties in confined geometries is developed. This includes scattering from a central field inside the guide created e.g. by impurities. For atomic collisions our approach applies to…
We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm…
The infrared singularities of scattering amplitudes have historically contributed to much development in understanding fundamental structures in physics. However, the fate of the leading soft singularities of amplitudes in non-trivial…
In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
One hundred years ago this year attempts began to generalise general relativity with the ambition of incorporating electromagnetism alongside gravitation in a unified field theory. These developments led to gauge theories and models with…
Cross-sections for particles scattered from selected spatial geometries exhibit many of the same interesting features as Mie scattering.
Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology,…
We describe a natural geometric relationship between matroids and underlying flag matroids by relating the geometry of the greedy algorithm to monotone path polytopes. This perspective allows us to generalize the construction of underlying…
In this paper we study an algebra that naturally combines two familiar operations in scattering amplitudes: computations of volumes of polytopes using triangulations and constructions of canonical forms from products of smaller ones. We…
In this thesis we present a study of the computation of classical observables in gauge theories and gravity directly from scattering amplitudes. In particular, we discuss the direct application of modern amplitude techniques in the one, and…
We explore novel connections between antimatroids and matchings in bipartite graphs. In particular, we prove that a combinatorial structure induced by stable matchings or maximum-weight matchings is an antimatroid. Moreover, we demonstrate…
The concept of quantum geometry for single-particle states has revolutionized our interpretation of several emergent properties in condensed matter. However, a description of the quantum geometry for interacting particles and an…
Scattering measurements with incident linearly polarized $\gamma$ rays provide information on spins, parities, and $\gamma$-ray multipolarity mixing coefficients, and, therefore, on the nuclear matrix elements involved in the transitions.…
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…
Scattering amplitudes of $\operatorname{tr}(\phi^3)$ theory can be encoded as the canonical form of the Stasheff associahedron. Similarly, the flat-space wavefunction coefficients of the same theory are captured by the recently proposed…
The story of positive geometry of massless scalar theories was pioneered in [1] in the context of bi-adjoint $\phi^3$ theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial…
A brief overview is given of some recent advances in charged-composite particle scattering. On the theoretical side, I address the three-charged particle wave function asymptotics, the nonperturbative investigation of the long-range…
We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection…
We investigate the gravitational multipole structure derived from scattering amplitudes in both four- and higher-dimensional spacetimes, with particular focus on the five-dimensional case. We develop a systematic procedure to extract…