相关论文: STR: a Mathematica package for the method of uniqu…

We investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble…

This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…

The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…

In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral $\mathrm{sl}(2,\mathbb{C})$ nature of spacetime. While our previous work…

An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…

Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric…

We study the symbology of planar Feynman integrals in dimensional regularization by considering geometric configurations in momentum twistor space corresponding to their leading singularities (LS). Cutting propagators in momentum twistor…

Loop-tree duality allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct comparison with real radiation terms. In this talk, we review the basis of the method and describe its application to…

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…

A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…

We take the first step in generalizing the so-called "Schubert analysis", originally proposed in twistor space for four-dimensional kinematics, to the study of symbol letters and more detailed information on canonical differential equations…

The traditional formulation of string amplitudes via worldsheet integrals provides a parametrization of the moduli space that fails to expose the complete singularity structure of the amplitudes. This problem is solved by the positive…

We present an exact analytical solution of the spectral problem of quasi one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that…

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package…

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…

We present an iterative method for generating the complete set of self-energy Feynman diagrams at arbitrary order for the single-polaron problem with arbitrary linear coupling to the lattice. The approach combines a combinatorial…

We give a simple tutorial introduction to the Mathematica package STRINGVACUA, which is designed to find vacua of string-derived or inspired four-dimensional N=1 supergravities. The package uses powerful algebro-geometric methods, as…

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…

The clustering and visualisation of high-dimensional data is a ubiquitous task in modern data science. Popular techniques include nonlinear dimensionality reduction methods like t-SNE or UMAP. These methods face the `scale-problem' of…

We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman…