Related papers: Amplituhedra, and Beyond
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Amplituhedra $\mathcal{A}_{n,k}^{(m)}$ are geometric objects of great interest in modern mathematics and physics: for mathematicians they are combinatorially rich generalizations of polygons and polytopes, based on the notion of positivity;…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
The field of scattering amplitudes plays a central role in elementary-particle physics. This includes various problems of broader interest for collider physics, gravitational physics, and fundamental principles underlying quantum field…
We define inclusive scattering matrix in the framework of geometric approach to quantum field theory . We review the definitions of scattering theory in the algebraic approach and relate them to the definitions in geometric approach.
The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in…
A central problem in quantum field theory is the computation of scattering amplitudes. However, traditional methods are impractical to calculate high order phenomenologically relevant observables. Building on a few decades of astonishing…
The amplituhedron is a semialgebraic set given as the image of the non-negative Grassmannian under a linear map subject to a choice of additional parameters. We define the limit amplituhedron as the limit of amplituhedra by sending one of…
Quantum field theory provides us with the means to calculate scattering amplitudes. In recent years a dramatic new development has lead to great simplification of such calculations. This is based on the discovery of the``amplituhedron'' in…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N=4 super-Yang-Mills theory, as well as (super)gravity. I also…
We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden "totally positive" structure strikingly similar to the positive…
We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical…
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…