Related papers: Quantum deformation of planar amplitudes
We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as $p^2 \to 0$. In particular, we study a form factor…
Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the…
On-shell diagrams are gauge invariant quantities which play an important role in the description of scattering amplitudes. Based on the principles of generalized unitarity, they are given by products of elementary three-point amplitudes…
We initiate an exploration of on-shell functions in $\mathcal{N}=4$ SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as…
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight…
We show that the half-integrands in the CHY representation of tree amplitudes give rise to the definition of differential forms -- the scattering forms -- on the moduli space of a Riemann sphere with $n$ marked points. These differential…
We study the ring theory of the multiparameter deformations of the quantum Schubert cell algebras obtained from 2-cocycle twists. This is a large family, which extends the Artin-Schelter-Tate algebras of twisted quantum matrices. We…
Categorification of scattering amplitudes for planar Feynman diagrams in scalar field theories with a polynomial potential is reported. Amplitudes for cubic theories are directly written down in terms of projectives of hearts of…
A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…
There is a remarkable well-known connection between the G$(4,n)$ cluster algebra and $n$-particle amplitudes in $\mathcal{N}=4$ SYM theory. For $n \ge 8$ two long-standing open questions have been to find a mathematically natural way to…
The way we organise perturbation theory is of fundamental importance both for computing the observables of relevance and for extracting fundamental physics out of them. If on one hand the different ways in which the perturbative observables…
Starting with the seminal work of Arkani-Hamed et al arXiv:1711.09102, in arXiv:1811.05904, the "Amplituhedron program" was extended to analyzing (planar) amplitudes in massless $\phi^{4}$ theory. In this paper we show that the program can…
Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved…
We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle…
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical…
We present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory. It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. Our…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experimental study of point counts over F_q modulo q^3, for graphs…
We build upon the prior works of [1-3] to study tree-level planar amplitudes for a massless scalar field theory with polynomial interactions. Focusing on a specific example, where the interaction is given by $\lambda_3\phi^{3}\ +\lambda_4…
The Amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the…