Related papers: A fresh look on three-loop sum-integrals
We present some new three-loop results in lattice gauge theories, for the Free Energy and for the Topological Susceptibility. These results are an outcome of a scheme which we are developing (using a symbolic manipulation language), for the…
It is explicitly shown, for optical processes arbitrarily comprising two-, three- or four-photon interactions, that the sum over all matter states of any optical susceptibility is exactly zero. The result remains true even in frequency…
In this paper, we present RTSUM, an unsupervised summarization framework that utilizes relation triples as the basic unit for summarization. Given an input document, RTSUM first selects salient relation triples via multi-level salience…
We present an analytical method to calculate the three-loop massive Feynman integral in arbitrary dimensions. The method is based on the Mellin-Barnes representation of the Feynman integral. The Meijer theorem and its corollary are used to…
We introduce the Mathematica package SummerTime for arbitrary-precision computation of sums appearing in the results of DRA method. So far these results include the following families of the integrals: 3-loop onshell massless vertices,…
I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and…
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…
I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…
An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and…
We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
With the advent of ultra-high power lasers the nonlinear nature of the vacuum of quantum electrodynamics (QED) can be probed. Due to the highly nonlinear structure of the underlying equations new numerical algorithms are required. A…
A large class of Feynman integrals, like e.g., two-point parameter integrals with at most one mass and containing local operator insertions, can be transformed to multi-sums over hypergeometric expressions. In this survey article we present…
In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…
We demonstrate the applicability of integration-by-parts (IBP) identities in finite-temperature field theory. As a concrete example, we perform 3-loop computations for the thermodynamic pressure of QCD in general covariant gauges, and…
Current methods to describe the thermodynamic behavior of many-particle systems are often based on perturbation theory with an unperturbed system consisting of free particles. Therefore, only a few methods are able to describe both strongly…
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
Some methods for the numerical computation of two-loop non-infrared vertices are reviewed. A new method is also proposed and compared to the old ones. Finally, some preliminary results are presented, concerning the evaluation of the…
Given the multitude of applications of vector vortex beams there is a need for robust tools to measure them. Here we exploit the non-separability of such beams, akin to entanglement of quantum states, to apply tools traditionally associated…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…