Related papers: Likelihood Equations and Scattering Amplitudes
When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and…
In the pure scattering theory, the universality of the soft limit has been studied for a long time. In this talk we review the property of soft limit to relate an $n$-point amplitude to an $(n-1)$-point amplitude. We show how this property…
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
These lecture notes bridge a gap between introductory quantum field theory (QFT) courses and state-of-the-art research in scattering amplitudes. They cover the path from basic definitions of QFT to amplitudes relevant for processes in the…
The asymptotic behavior of the elastic scattering amplitude by the exchange of graviton between two scalar particles at high energies and fixed momentum transfers is reconsidered in the Logunov-Tavkhelidze equation in the linearized…
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We…
The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is…
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…
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…
Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…
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…
Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
Several recent developments point to the fact that rational maps from n-punctured spheres to the null cone of D dimensional momentum space provide a natural language for describing the scattering of massless particles in D dimensions. In…
We compute the semi-classical potential arising from a generic theory of cubic gravity, a higher derivative theory of spin-2 particles, in the framework of modern amplitude techniques. We show that there are several interesting aspects 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…