Related papers: Intersection theory rules symbology
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
We consider a primitive distance-regular graph $\Gamma$ with diameter at least $3$. We use the intersection numbers of $\Gamma$ to find a positive semidefinite matrix $G$ with integer entries. We show that $G$ has determinant zero if and…
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm starts with…
This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular…
We present an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their individual segments, reducing the number of diagrams needed to be calculated. The important step lies in the observation that…
We introduce a category of filtered F-isocrystals and construct a symbol maps on Milnor K-theory which is compatible with the syntomic symbol maps to the log syntomic cohomology. These are fundamental materials in our applications on…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
This article gives a short step-by-step introduction to the representation of parametric Feynman integrals in scalar perturbative quantum field theory as periods of motives. The application of motivic Galois theory to the algebro-geometric…
Let I be an arbitrary ideal in C[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal…
The intersection numbers of p-spin curves are computed through correlation functions of Gaussian ensembles of random matrices in an external matrix source. The p-dependence of intersection numbers is determined as polynomial in p; the large…
Following the renewed interest in the topic [1], we revisit the problem of assigning probabilities to classes of Feynman paths passing through specified space-time regions. We show that by assigning of probabilities to interfering…
This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…
In the well-studied genus zero case, bases of $\mathrm{d}\log$ integrands with integer leading singularities define Feynman integrals that automatically satisfy differential equations in canonical form. Such integrand bases can be…
We derive a full Bern-Kosower-type rule for scalar QED starting from quantum field theory: we derive a set of rules for calculating $S$-matrix elements for any processes at any order of the coupling constant. Gauge-invariant set of diagrams…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable…
We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization. The algorithm…
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…
Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms -- whose properties as…
Let $G$ be a finite, simple, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(\mathrm{diag}(\mathbf{d})-A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We…