The elliptic dilogarithm for the sunset graph
From MaRDI portal
Publication:479600
DOI10.1016/j.jnt.2014.09.032zbMath1319.81044arXiv1309.5865OpenAlexW2091996036MaRDI QIDQ479600
Publication date: 5 December 2014
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1309.5865
Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Variation of Hodge structures (algebro-geometric aspects) (14D07) Motivic cohomology; motivic homotopy theory (14F42)
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Uses Software
Cites Work
- Algebraic \(K\)-theory of toric hypersurfaces
- Hypergeometric representation of the two-loop equal mass sunrise diagram
- Feynman amplitudes and Landau singularities for one-loop graphs
- On the Picard-Fuchs equation and the formal Brauer group of certain elliptic \(K3\)-surfaces
- On motives associated to graph polynomials
- Analytic treatment of the two loop equal mass sunrise graph
- Generalized unitarity and one-loop amplitudes in \(\mathcal N=1\) super-Yang-Mills
- Two-loop sunset diagrams with three massive lines
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- The Bloch-Wigner-Ramakrishnan polylogarithm function
- Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters
- Quantum field theory techniques in graphical enumeration
- A second-order differential equation for the two-loop sunrise graph with arbitrary masses
- Picard-Fuchs equations for Feynman integrals
- On the differentiation of De Rham cohomology classes with respect to parameters
- Théorie de Hodge. II. (Hodge theory. II)
- Théorie de Hodge. III
- Evaluating Feynman integrals.
- Loop amplitudes in gauge theories: modern analytic approaches
- The Dilogarithm Function
- Elliptic integral evaluations of Bessel moments and applications
- Higher Regulators, Algebraic 𝐾-Theory, and Zeta Functions of Elliptic Curves
- A geometrical angle on Feynman integrals
- The two-loop sunrise graph with arbitrary masses
- Hypergeometric Forms for Ising-Class Integrals
- The Abel–Jacobi map for higher Chow groups
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