Related papers: Likelihood Equations and Scattering Amplitudes
In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…
The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target…
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique…
We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
The dependence of singularities of scattering matrices of the abstract wave equation on the choice of asymptotically equivalent outgoing/incoming subspaces is studied. The obtained results are applied to the radial wave equation with…
A formal relationship between scattering amplitudes in critical bosonic string theory and correlation functions of operators in topological string theory is found.
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitational-wave physics. Amplitude methods and insights are now employed for precision computations of…
The scattering amplitudes of string theory exhibit many extraordinary properties. But are they the unique mathematical objects to do so? Recently, it has been shown how the spectrum and amplitudes of open string theory follow directly from…
We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory.…
We propose an effectively nonperturbative approach to calculating scattering amplitudes in the perturbative regime. We do this in a discretized momentum space by using the QSE method to calculate all the contributions (to all orders in…
The analyticity properties of the scattering amplitude for a massive scalar field is reviewed in this article where the spacetime geometry is $R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigated the analyticity of…
This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure…
We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of $\pi^+$…
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…
The determination of magnitudes of basic parameters of the high energy elastic scattering amplitude are examined at small momentum transfers with taking account of the Coulomb-hadron interference effects.
Calculations of $1\to N$ amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number $N$ of final state particles. This either indicates an end of perturbative behaviour, or possibly…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle…