Related papers: The combinatorial geometry of particle physics
We derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphism-breaking corrections. We…
We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations…
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via techniques from polyhedral geometry. It turns out that the…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
The behavior of the hadron scattering amplitude determined by the gravitation interaction of hadron at high energies with impact of the KK-modes in d-brane models of gravity is examined. The possible periodic structure of the scattering…
In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…
Collective coherent light scattering by polarizable particles creates surprisingly strong, long range inter-particle forces originating from interference of the light scattered by different particles. While for monochromatic laser beams…
This thesis develops a unified framework that reconstructs the full classical content of General Relativity from the classical limit of quantum scattering amplitudes. By interpreting the analytic structure of amplitudes as the…
This article is a survey of matroid theory aimed at algebraic geometers. Matroids are combinatorial abstractions of linear subspaces and hyperplane arrangements. Not all matroids come from linear subspaces; those that do are said to be…
Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…
We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…
We propose a novel theoretical framework for barycentric interpolation, using concepts recently developed in mathematical physics. Generalized barycentric coordinates are defined similarly to Shepard's method, using positive geometries -…
Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a…
We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…