Related papers: Calculating Three Loop Ladder and V-Topologies for…
In this letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional to N_F^2, N_F*N, and N_F/N.…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The…
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…
We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…
We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and…
We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop orders. Interestingly, one of…
We will use commutators to provide decompositions of $3\times 3$ matrices as sums whose terms satisfy some polynomial identities, and we apply them to bounded linear operators and endomorphisms of free modules of infinite rank. In…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and (seven-point) double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $D_2\simeq A_1^2$, we…
In this article, we develop tools for computing $G$-crossed extensions of braided tensor categories. Their equivariantisations appear as categories of modules of fixed-point subalgebras (or orbifolds) of vertex operator algebras and are…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
We consider special Lambert series as generating functions of divisor sums and determine their complete transseries expansion near rational roots of unity. Our methods also yield new insights into the Laurent expansions and modularity…
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…
In this paper, we give matrix formulae for non-orientable surfaces that provide the Laurent expansion for quasi-cluster variables, generalizing the orientable surface matrix formulae by Musiker-Williams. We additionally use our matrix…
Evolution equations for leading twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry…
Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD…
We study QED corrections to operator matrix elements involving heavy composite particles (e.g., heavy-mesons, nuclei, and atoms). We define a new notion of reducible and irreducible graphs which is useful for systems with many discrete…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…