Results 11 to 20 of about 1,325 (265)
Elliptic Feynman integrals and pure functions
Journal of High Energy Physics, 2019 We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term.
Johannes Broedel +4 more
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On epsilon factorized differential equations for elliptic Feynman integrals
Journal of High Energy Physics, 2022 In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by integrating the ...
Hjalte Frellesvig
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
Journal of High Energy Physics, 2018 We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic ...
Johannes Broedel +4 more
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Master integrals for bipartite cuts of three-loop photon self energy
Journal of High Energy Physics, 2021 We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy.
R. N. Lee, A. I. Onishchenko
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Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism
Journal of High Energy Physics, 2018 We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have ...
Johannes Broedel +3 more
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Functional Inequalities for Generalized Complete Elliptic Integrals with Two Parameters
Journal of Function Spaces, 2019 In this paper, we establish some functional inequalities for generalized complete elliptic integrals with two parameters, such as estimation of bounds and mean inequalities.
Xiangkai Dou, Li Yin, Xiu-Li Lin
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Nuclear Physics B, 2017 We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve.
Christian Bogner +2 more
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Approximations related to the complete p-elliptic integrals
Open Mathematics, 2022 In this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations ...
Zhong Genhong, Ma Xiaoyan, Wang Fei
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SciPost Physics Proceedings, 2022 We discuss the analytic structure of the master integrals relevant for computing the com- plete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two loops in QCD.
Ekta Chaubey
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Singular Integral Operators and Elliptic Boundary-Value Problems. I
Современная математика: Фундаментальные направления, 2017 The book consists of three Parts I-III and Part I is presented here. In this book, we develop a new approach mainly based on the authors papers. Many results are published here for the first time. Chapter 1 is introductory.
Alexandre P Soldatov
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