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Loop-Tree Duality (LTD) is a framework in which the energy components of all loop momenta of a Feynman integral are integrated out using residue theorem, resulting in a sum over tree-like structures.
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J. J. Aguilera-Verdugo, F. Driencourt-Mangin, J. Plenter, S. Ramírez-Uribe, G. Rodrigo, G. F. Sborlini, W. J. Torres Bobadilla, and S. Tracz, Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders
1904
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T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
1905
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Z. Capatti, V. Hirschi, D. Kermanschah, and B. Ruijl, Loop Tree Duality for multi-loop numerical integration
1906
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1907
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1910
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1912
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J. J. Aguilera-Verdugo, F. Driencourt-Mangin, R. J. Hernandez Pinto, J. Plenter, S. Ramirez-Uribe, A. E. Renteria Olivo, G. Rodrigo, G. F. Sborlini, W. J. Torres Bobadilla, and S. Tracz, Open loop amplitudes and causality to all orders and powers from the loop-tree duality
2001
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F. C. S. Brown, Polylogarithmes multiples uniformes en une variable
2004
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A. V. Smirnov and V. A. Smirnov, Applying Grobner bases to solve reduction problems for Feynman integrals
2006
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2014
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J. J. Aguilera-Verdugo, R. J. Hernandez-Pinto, G. Rodrigo, G. F. Sborlini, and W. J. Torres Bobadilla, Causal representation of multi-loop amplitudes within the loop-tree duality
2006
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S. Ramírez-Uribe, R. J. Hernández-Pinto, G. Rodrigo, G. F. Sborlini, and W. J. Torres Bobadilla, Universal opening of four-loop scattering amplitudes to trees
2006
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C. Anastasiou, S. Beerli, and A. Daleo, Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
2007
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A. Lazopoulos, K. Melnikov, and F. Petriello, QCD corrections to tri-boson production
2007
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C. Anastasiou, K. Melnikov, and F. Petriello, The Electron energy spectrum in muon decay through O(alpha**2)
2007
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R. N. Lee, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
2008
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C. Anastasiou, S. Beerli, and A. Daleo, The Two-loop QCD amplitude gg —¿ h,H in the Minimal Supersymmetric Standard Model
2008
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T. Peraro, Scattering amplitudes over finite fields and multivariate functional reconstruction
2016
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P. Mastrolia, T. Peraro, and A. Primo, Adaptive Integrand Decomposition in parallel and orthogonal space
2016
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2016
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G. F. R. Sborlini, F. Driencourt-Mangin, R. Hernandez-Pinto, and G. Rodrigo, Four-dimensional unsubtraction from the loop-tree duality
2016
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L. Mantovani, B. Pasquini, X. Xiong, and A. Bacchetta, Revisiting the equivalence of light-front and covariant qed in the light-cone gauge
2016
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G. Passarino, Elliptic Polylogarithms and Basic Hypergeometric Functions
2017
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E. Remiddi and L. Tancredi, An Elliptic Generalization of Multiple Polylogarithms
2017
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J. Boehm, A. Georgoudis, K. J. Larsen, M. Schulze, and Y. Zhang, Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
2018
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D. A. Kosower, Direct Solution of Integration-by-Parts Systems
2018
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J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C. Raab, C. Radu, and C. Schneider, Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
2018
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S. Borowka, G. Heinrich, S. Jahn, S. P. Jones, M. Kerner, J. Schlenk, and T. Zirke, pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
2018
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C. Anastasiou and G. Sterman, Removing infrared divergences from two-loop integrals
2019
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D. Kermanschah, Subtracting Threshold Singularities at One Loop
2020
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Z. Capatti, V. Hirschi, A. Pelloni, and B. Ruijl, Local Unitarity: A representation of differential cross-sections that is locally free of infrared singularities at any order
2020
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A. B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes
2076
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