Related papers: Feynman Integral Relations from GKZ Hypergeometric…
We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within…
We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of…
The Zippel algorithm performs a rational reconstruction of multivariate polynomials and aims specifically at the sparse case. It is applied in different fields of science, lately becoming an important step in Feynman integral reduction in…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
We study the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky and its relationship with the toric Deligne-Mumford (DM) stacks recently studied by Borisov, Chen and Smith. We construct series solutions with…
In this article, we construct two-dimensional integrable and superintegrable sys- tems in terms of the master function formalism and relate them to Mielnik;s and Marquette;s construction in supersymmetric quantum mechanics. For two diferent…
This article provides a conceptual and historical review of the evolution of integrable Hamiltonian systems from the Moscow School of A. T. Fomenko to the emerging Azarbaijan School of Geometric Dynamical Systems founded by the author.…
High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we…
We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a…
We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…
We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can…
We consider the $sl(2)$ quantized Knizhnik-Zamolodchikov equation (qKZ), defined in terms of rational R-matrices. The properties of the equation change when the step of the equation takes a resonance value. In this case the discrete…