Related papers: Iterated integrals over higher dimensional loops
In this paper we continue the development of the differential calculus started by Aragona-Ferandez-Juriaans. Guided by the topology introduced recently by those authors we introduce the notion of membranes and extend the definition of…
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing "invariant versions" of iterated integrals of modular forms. The construction will be based on an extension of…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest…
We introduce the notion of iterated group extensions, which, roughly speaking, is what one obtains by forming a group extension of a group extension. We interpret iterated extensions in terms of group cohomology, in the same way as…
We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…
We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by $z^{s-1}$, along geodesics connecting two cusps. This setting generalizes simultaneously the…
We introduce a novel notion of pasting shapes for iterated Segal spaces which classify particular arrangements of composing cells in d-uple Segal spaces. Using this formalism, we then continue to prove a pasting theorem for these iterated…
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.
Motivated by amplitude calculations in string theory we establish basic properties of homotopy invariant iterated integrals on affine curves.
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…