Related papers: Tropical Amplitudes For Colored Lagrangians
Multiloop scattering amplitudes describing the quantum fluctuations at high-energy scattering processes are the main bottleneck in perturbative quantum field theory. The loop-tree duality is a novel method aimed at overcoming this…
Following the proposal of arXiv:1312.6673, multi-particle scattering amplitudes are represented as conserved higher-spin charges. The advantage of such reformulation is that multi-particle amplitudes acquire the form of an integral of a…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
The scattering amplitudes for colored scalars can be calculated using the so-called curve integral formula, relying on simple combinatorics. It introduces a set of global Schwinger parameters for all Feynman diagrams that contribute to an…
In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of…
The calculation of scattering amplitudes in Yang-Mills theory at loop level is important for the analysis of background processes at particle colliders as well as our understanding of perturbation theory at the quantum level. We present…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
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…
We revisit the relations between open and closed string scattering amplitudes discovered by Kawai, Lewellen, and Tye (KLT). We show that they emerge from the underlying algebro-topological identities known as the twisted period relations.…
A surprising connection has recently been made between the amplitudes for Tr($\Phi^3$) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of…
Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles - the Tr$(\phi^3)$ theory - based on combinatorial and geometric ideas in the kinematic space of…
Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis…
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…
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…
We consider scattering by short range perturbations of the semi-classical Laplacian. We prove that when a polynomial bound on the resolvent holds, the scattering amplitude is a semi-classical Fourier integral operator associated to the…
Scattering amplitudes for colored theories have recently been formulated in a new way, in terms of curves on surfaces. In this note we describe a canonical set of functions we call surface functions, associated to all orders in the…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
We present compact analytic formulae for the one-loop amplitudes for Higgs + 4 parton scattering, $0 \to g g g g h$, $0 \to \bar{q} q gg h$ and $0\to \bar{q} q \bar{q}^\prime q^\prime h$, mediated by a loop of massive coloured quarks. We…