Related papers: On Positive Geometry and Scattering Forms for Matt…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…
We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully…
We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm…
We introduce a new dynamical group whose coadjoint action on its momentum space takes account of matter-antimatter symmetry on pure geometrical grounds. According to this description the energy and the spin are unchanged under…
We extend the T-matrix approach to light scattering by spherical particles to some simple cases in which the scatterers are optically anisotropic. Specifically we consider cases in which the spherical particles include radially and…
The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a…
We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional…
We examine scattering amplitudes for an arbitrary number of photons in a class of non-null background electromagnetic fields, studying tree-level and one-loop amplitudes in scalar and spinor quantum-electrodynamics in backgrounds defined by…
A geometric approach to understanding recursion relations for scattering amplitudes is developed. We achieve this by studying intersection numbers of triangulated accordiohedra presented as hyperplane arrangements. The cancellation of…
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…
This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general off-shell…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
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…
In this paper we explore and expand the connection between two modern descriptions of scattering amplitudes, the CHY formalism and the framework of positive geometries, facilitated by the scattering equations. For theories in the CHY family…
Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field…
We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in…
This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the…
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…
The Buchholz' scattering theory of waves in two dimensional massless models suggests a natural definition of a scattering amplitude. We compute such a scattering amplitude for charged infraparticles that live in the GNS representation of…
We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method…