相关论文: Feynman Diagrams, Differential Reduction, and Hype…

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…

The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…

The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by…

After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary…

We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.

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…

The symmetry factor of Feynman diagrams for real and complex scalar fields is presented. Being analysis of Wick expansion for Green functions, the mentioned factor is derived in a general form. The symmetry factor can be separated into two…

We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are A-hypergeometric functions of coefficients of polynomial…

Just as with the Gauss hypergeometric function, particular cases of the local Heun function can be Liouvillian (that is, "elementary") functions. One way to obtain these functions is by pull-back transformations of Gauss hypergeometric…

We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the…

Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge…

In this work we present the relation between method of brackets and the master theorem of Ramanujan in the evaluation of multivariable integrals, in this case Feynman diagrams.

We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the…

In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent hypergeometric functions of two variables $F_4$. These are defined for…

The reductions of the Heun equation to the hypergeometric equation by polynomial transformations of its independent variable are enumerated and classified. Heun-to-hypergeometric reductions are similar to classical hypergeometric…

The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…

We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable -- the geodesic distance. But now this dependence…