Related papers: Amplituhedra, and Beyond
On-shell methods have revitalized interest in scattering amplitudes which have, in turn, shed some much needed light on the structure of quantum field theories. These developments have been warmly embraced by the particle physics community.…
We formulate the field-space geometry for an effective field theory of scalars and gauge bosons. Geometric invariants such as the field-space curvature enter in both scattering amplitudes and the renormalization group equations, with the…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
The tree amplituhedra $\mathcal{A}_{n,k}^{(m)}$ are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for $m=4$ as a geometric construction encoding tree-level scattering amplitudes in planar…
We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized…
In recent years, it has been understood that color-ordered scattering amplitudes can be encoded as logarithmic differential forms on positive geometries. In particular, amplitudes in maximally supersymmetric Yang-Mills theory in spinor…
The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
In this paper we study a relation between two positive geometries: the momentum amplituhedron, relevant for tree-level scattering amplitudes in $\mathcal{N} = 4$ super Yang-Mills theory, and the kinematic associahedron, encoding tree-level…
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.…
Twists of four-dimensional supersymmetric quantum field theories (SQFTs) isolate protected sectors with rich algebraic structures. We develop a unified framework for analyzing symmetries and anomalies in four-dimensional holomorphically…
We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar N=4 SYM. We show how the textbook structure of the unitarity double-cut…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of…
In this paper the authors seek to trace in an accessible fashion the rapid recent development of the theory of the matrix geometric mean in the cone of positive definite matrices up through the closely related operator geometric mean in the…
Positive geometry provides a geometric framework where physical observables are encoded as canonical forms associated to regions of kinematic space. In this paper we consider a generalisation to an infinite union of line segments, which…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…