Related papers: A fresh look on three-loop sum-integrals
We present conditions for the efficient simulation of a broad class of optical quantum circuits on a classical machine: this class includes unitary transformations, amplification, noise, and measurements. Various proposed schemes for…
In this paper we propose and demonstrate the potential for unifying models and algorithms for the steady state and transient simulation of single-phase and three-phase power systems. At present, disparate algorithms and models are used for…
Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $\epsilon…
Using a recently developed three-point formalism within the method of QCD Sum Rules we determine the vacuum susceptibilities needed in the two-point formalism for the coupling of axial, vector, tensor and pseudoscalar currents to hadrons.…
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops.…
Three-loop quantum corrections to the effective action are calculated for N=1 supersymmetric electrodynamics, regularized by higher derivatives. Using the obtained results we investigate the anomaly puzzle in the considered model.
A method for evaluating finite trigonometric summations is applied to a system of N coupled oscillators under acceleration. Initial motion of the nth particle is shown to be of the order ${{T}^{2n+2}}$ for small time T and the end particle…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
The 3PI method is a technique to resum an infinite class of diagrams, which may be useful in studying nonperturbative thermodynamics and dynamics in quantum field theory. But it has never been successfully applied to gauge theories, where…
We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order…
We consider a massive relativistic Bose gas with $N$ complex scalars at finite density. At zero temperature, we calculate the pressure, charge density and the speed of sound in the one-loop approximation. In the nonrelativistic limit, we…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous…
We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman…
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and…
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…
In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…
It is often difficult to quantitatively determine if a new molecular simulation algorithm or software properly implements sampling of the desired thermodynamic ensemble. We present some simple statistical analysis procedures to allow…
We present compact, fully analytical expressions for singular parts of a class of three-loop diagrams which cannot be factorized into lower-loop integrals. As a result of the calculations we obtain the analytical expression for the…