相关论文: Tensor structure from scalar Feynman matroids

We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its…

We study a rational matroid invariant, obtained as the tropicalization of the Feynman period integral. It equals the volume of the polar of the matroid polytope and we give efficient formulas for its computation. This invariant is proven to…

This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. The frame uses the notion of matroids. For the proof of the existence of the…

In this paper, we explore the recursive structure of Baikov representations for Feynman integrals. We demonstrate that the various Baikov representations for all sectors of an integral family can be organized in a tree-like structure. Using…

Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products…

Single scale Feynman integrals in quantum field theories obey difference or differential equations with respect to their discrete parameter $N$ or continuous parameter $x$. The analysis of these equations reveals to which order they…

An invariant theoretic characterization of subdiscriminants of matrices is given. The structure as a module over the special orthogonal group of the minimal degree non-zero homogeneous component of the vanishing ideal of the variety of real…

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…

For each object in a tensor triangulated category, we construct a natural continuous map from the object's support---a closed subset of the category's triangular spectrum---to the Zariski spectrum of a certain commutative ring of…

We propose a scalar-tensor representation of $f(R)$ theories with use of conformal transformations. In this representation, the model takes the form of the Brans-Dicke model with a potential function and a non-zero kinetic term for the…

We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…

Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…

We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these…

We present the lattice structure of Feynman diagram renormalization in physical QFTs from the viewpoint of Dyson-Schwinger-Equations and the core Hopf algebra of Feynman diagrams. The lattice structure encapsules the nestedness of diagrams.…

We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass…

In this paper, we study various properties of matroidal ideals.

This talk reviews Feynman integrals, which are associated to elliptic curves. The talk will give an introduction into the mathematics behind them, covering the topics of elliptic curves, elliptic integrals, modular forms and the moduli…

We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical…

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…