Related papers: Amplituhedra, and Beyond
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
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…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
We consider the theory of \emph{twisted symmetries} of differential equations, in particular $\lambda$ and $\mu$-symmetries, and discuss their geometrical content. We focus on their interpretation in terms of gauge transformations on the…
This chapter introduces the foundational elements of scattering amplitudes. It is meant to be accessible to readers with only a basic understanding of quantum field theory. Topics covered include: the four-dimensional spinor-helicity…
In this brief review, we report on the status of asymptotic symmetries of gravity corresponding to the class of metrices named asymptotically flat spacetimes in higher (d > 4) dimensions. We discuss the consequences of these symmetries both…
Scattering amplitudes have their origin in quantum field theory, but have wide-ranging applications extending to classical physics. We review a formalism to connect certain classical observables to scattering amplitudes. An advantage of…
I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…
In this paper we focus on scattering amplitudes in maximally supersymmetric Yang-Mills theory and define a long sought-after geometry, the loop momentum amplituhedron, which we conjecture to encode tree and (the integrands of) loop…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
We present a pedagogical review of particle physics models that are based on the noncommutativity of space-time, $[\hat{x}_\mu,\hat{x}_\nu]=i \theta_{\mu \nu}$, with specific attention to the phenomenology these models predict in particle…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
It has been a long-standing challenge to find a geometric object underlying the cosmological wavefunction for Tr($\phi^3$) theory, generalizing associahedra and surfacehedra for scattering amplitudes. In this note we describe a new class of…
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…
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics…
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…