Related papers: A geometrical framework for amplitude recursions: …
Attached to both Yang-Mills and General Relativity about Minkowski spacetime are distinguished gauge independent objects known as the on-shell tree scattering amplitudes. We reinterpret and rigorously construct them as $L_\infty$ minimal…
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations…
We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums…
Conventional approaches for scattering manipulations rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is non-generic (expansion coefficients depend on the position of the…
We study the self-similar structure of loop amplitudes in quantum field theory and apply it to amplitude generation and renormalization. A renormalized amplitude can be regarded as an effective coupling that recursively appears within…
Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit,…
Framework materials and their deformations provide a compelling relation between materials science and algebraic geometry. Physical distance constraints within the material transform into polynomial constraints, making algebraic geometry…
We present all-multiplicity formulae, derived from first principles in the MHV sector and motivated by twistor string theory for general helicities, for the tree-level S-matrix of gluon scattering on self-dual radiative backgrounds. These…
It is well-known that perturbative calculations in field theory can lead to far simpler answers than the Feynman diagram approach might suggest. In some cases scattering amplitudes can be constructed for processes with any desired number of…
This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random…
Using light cone string field theory we derive recursion relations for closed string correlation functions and scattering amplitudes which hold to all orders in perturbation theory. These results extend to strings in a plane wave…
The search for a theory of the S-Matrix has revealed surprising geometric structures underlying amplitudes ranging from the worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to kinematic space…
If scattering amplitudes are ordinary complex numbers (not quaternions) there is a universal algebraic relationship between the six coherent cross sections of any three scatterers (taken singly and pairwise). A violation of this…
In this thesis, we study the properties of String theory amplitudes within the framework of Intersection Theory (IT) for twisted (co)homology, which, as recently proposed, offered a novel approach to analyze relations between scattering…
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…
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the…