Related papers: First Results with a new Method for calculating 2-…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…
The scalar one-loop 4-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method a characteristic scale $\mu_{s}$ is introduced to regularize the divergent…
We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
In this article, we present a new analytic result for a certain single-mass-scale four-loop vacuum (bubble) integral. We also discuss its systematic $\e$-expansion in $d=4-2\e$ as well as $d=3-2\e$ dimensions, the coefficients of which are…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…
The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new…
Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic…
The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional…
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…
We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane.…
For a three-dimensional higher-derivative scalar superfield model, and a four-dimensional higher-derivative chiral superfield model, where which the higher-derivative operators are described by polynomials of arbitrary degrees, we…
Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrated by obtaining a closed-form expression for the value of an…
We propose a new approach to the computation of the hypervolume indicator, based on partitioning the dominated region into a set of axis-parallel hyperrectangles or boxes. We present a nonincremental algorithm and an incremental algorithm,…
We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
We examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…