Related papers: The five-twist identity for Feynman periods
The Symmetries of Feynman Integrals (SFI) is a method for evaluating Feynman Integrals which exposes a novel continuous group associated with the diagram which depends only on its topology and acts on its parameters. Using this method we…
The article is an overview of the role of graph complexes in the Feynman path integral quantization. The underlying mathematical language is that of PROPs and operads, and their representations. The sum over histories approach, the Feynman…
The Fisher transformation acts on cubic graphs by replacing each vertex by a triangle. We explore the action of the Fisher transformation on the set of self-avoiding walks of a cubic graph. Iteration of the transformation yields a sequence…
Let p be a prime number, F a totally real field such that [F(mu_p): F]=2 and [F:Q] is odd. For delta \in F^times, let [delta] denote its class in F^times/F^{times p}. In this paper, we show Main Theorem. There are infinitely many classes…
A long-standing conjecture in quantum field theory due to Broadhurst and Kreimer states that the amplitudes of the zig-zag graphs are a certain explicit rational multiple of the odd values of the Riemann zeta function. In this paper we…
We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
Graphical functions are special position space Feynman integrals, which can be used to calculate Feynman periods and one- or two-scale processes at high loop orders. With graphical functions, renormalization constants have been calculated…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…
A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of…
Two fundamental theta identities, a three-term identity due to Weierstrass and a five-term identity due to Jacobi, both with products of four theta functions as terms, are shown to be equivalent. One half of the equivalence was already…
A family of nonhermitian quantum graphs (exhibiting, presumably, a hidden form of hermiticity) is proposed and studied via their discretization.
Spherical contours introduced in \cite{SphericalContours} translate the concept of "discontinuity across a branch cut" to Feynman parameter space. In this paper, we further explore spherical contours and connect them to the computation of…
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…
We discuss, on general grounds, how two subgraphs of a given Feynman graph can overlap with each other. For this, we use the notion of connecting and returning lines that describe how any subgraph is inserted within the original graph.…
We derive a "switching identity" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster configurations and at the more general level of the…
This paper presents a new family of almost identities. These are based on series that sum to elements close to either rationals or rational multiples of pi. The explanation of the phenomenon takes its roots in the theory of Mellin…
In this work, we analyze vanishing cycles of Feynman loop integrals by means of the Mayer-Vietoris spectral sequence. A complete classification of possible vanishing geometries are obtained. We employ this result for establishing an…
We characterise all vertex-transitive finite connected graphs as essentially 5-connected or on a short list of explicit graph-classes. Our proof heavily uses Tutte-type canonical decompositions.