Related papers: The analytic structure of three-point functions fr…
The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation…
Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…
In two-dimensional models of critical non-intersecting loops, there are $\ell$-leg fields that insert $\ell\in\mathbb{N}^*$ open loop segments, and diagonal fields that change the weights of closed loops. We conjecture an exact formula for…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
Contour integration is a crucial technique in many numeric methods of interest in physics ranging from differentiation to evaluating functions of matrices. It is often important to determine whether a given contour contains any poles or…
In this paper we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows to represent a deformation field in a coordinate-free way…
Contour integrals of rational functions over ${\cal M}_{0,n}$, the moduli space of $n$-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined…
We investigate the analytic structure of functions defined by integrals with integrands singular on a finite union of quadrics. The main motivation comes from Feynman integrals which belong to this class. Using isotopy techniques we derive…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], where it is stated…
In this article, we explore the use of contour deformation for the numerical evaluation of Feynman integrals after sector decomposition. In existing codes, the contour of integration is determined heuristically for each phase-space point by…
We present a comprehensive method for the evaluation of a vast class of integrals representing 3-point functions of conformal field theories in momentum space. The method leads to analytic, closed-form expressions for all scalar and…
We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the…
We show how to construct embedding space three-point functions for operators in arbitrary Lorentz representations by employing the formalism developed in arXiv:1905.00036 and arXiv:1905.00434. We study tensor structures that intertwine the…
In this paper we present a novel technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. In order to extract…
In this paper we develop a general method for constructing 3-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on 2-point functions. The results are provided in terms of triangular…
Contour integral algorithms seek to compute a small number of eigenvalues located within a bounded region of the complex plane. These methods can be applied to both linear and nonlinear matrix eigenvalue problems. In the latter case, the…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
We study the occurrence of curved three-point configurations in fractal subsets of the real line. We prove that if \(E \subset [0,1]\) is a compact set with sufficiently large Hausdorff dimension, then \(E\) contains a curved three-point…