Relevant bibliographies by topics / Multi-loop Feynman integrals

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Multi-loop Feynman integrals'

Author: Grafiati
Published: 6 September 2023
Last updated: 31 July 2025

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Journal articles on the topic "Multi-loop Feynman integrals"

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Smirnov, Vladimir A., and Matthias Steinhauser. "Solving recurrence relations for multi-loop Feynman integrals." Nuclear Physics B 672, no. 1-2 (2003): 199–221. http://dx.doi.org/10.1016/j.nuclphysb.2003.09.003.

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Isaev, A. P. "Multi-loop Feynman integrals and conformal quantum mechanics." Nuclear Physics B 662, no. 3 (2003): 461–75. http://dx.doi.org/10.1016/s0550-3213(03)00393-6.

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Baikov, P. A. "Criterion of irreducibility of multi-loop Feynman integrals." Physics Letters B 474, no. 3-4 (2000): 385–88. http://dx.doi.org/10.1016/s0370-2693(00)00053-8.

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Zhou, Yajun. "Wick rotations, Eichler integrals, and multi-loop Feynman diagrams." Communications in Number Theory and Physics 12, no. 1 (2018): 127–92. http://dx.doi.org/10.4310/cntp.2018.v12.n1.a5.

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Aguilera-Verdugo, José de Jesús, Félix Driencourt-Mangin, Roger José Hernández-Pinto, et al. "A Stroll through the Loop-Tree Duality." Symmetry 13, no. 6 (2021): 1029. http://dx.doi.org/10.3390/sym13061029.

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The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.
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Preti, Michelangelo. "STR: A Mathematica package for the method of uniqueness." International Journal of Modern Physics C 31, no. 10 (2020): 2050146. http://dx.doi.org/10.1142/s0129183120501466.

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We present Star–Triangle Relations (STRs), a Mathematica® package designed to solve Feynman diagrams by means of the method of uniqueness in any Euclidean space-time dimension. The method of uniqueness is a powerful technique to solve multi-loop Feynman integrals in theories with conformal symmetry imposing some relations between the powers of propagators and the space-time dimension. In our algorithm, we include both identities for scalar and Yukawa type integrals. The package provides a graphical environment in which it is possible to draw the desired diagram with the mouse input and a set o
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Kastening, Boris, and Hagen Kleinert. "Efficient algorithm for perturbative calculation of multi-loop Feynman integrals." Physics Letters A 269, no. 1 (2000): 50–54. http://dx.doi.org/10.1016/s0375-9601(00)00199-7.

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Baikov, P. A. "A practical criterion of irreducibility of multi-loop Feynman integrals." Physics Letters B 634, no. 2-3 (2006): 325–29. http://dx.doi.org/10.1016/j.physletb.2006.01.052.

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Goode, Jae, Franz Herzog, and Sam Teale. "OPITeR: A program for tensor reduction of multi-loop Feynman integrals." Computer Physics Communications 312 (July 2025): 109606. https://doi.org/10.1016/j.cpc.2025.109606.

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Jurčišinová, E., and M. Jurčišin. "A general formula for analytic reduction of multi-loop tensor Feynman integrals." Physics Letters B 692, no. 1 (2010): 57–60. http://dx.doi.org/10.1016/j.physletb.2010.07.018.

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Dissertations / Theses on the topic "Multi-loop Feynman integrals"

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Meyer, Christoph. "Algorithmic transformation of multi-loop Feynman integrals to a canonical basis." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/18763.

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Die Auswertung von Mehrschleifen-Feynman-Integralen ist eine der größten Herausforderungen bei der Berechnung präziser theoretischer Vorhersagen für die am LHC gemessenen Wirkungsquerschnitte. In den vergangenen Jahren hat sich die Nutzung von Differentialgleichungen bei der Berechnung von Feynman-Integralen als sehr erfolgreich erwiesen. Es wurde dabei beobachtet, dass die von den Feynman-Integralen erfüllte Differentialgleichung oftmals in eine sogenannte kanonische Form transformiert werden kann, welche die Integration der Differentialgleichung mittels iterierter Integrale wesentlich verein
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Meyer, Christoph [Verfasser], Peter [Gutachter] Uwer, Dirk [Gutachter] Kreimer, and Stefan [Gutachter] Weinzierl. "Algorithmic transformation of multi-loop Feynman integrals to a canonical basis / Christoph Meyer ; Gutachter: Peter Uwer, Dirk Kreimer, Stefan Weinzierl." Berlin : Humboldt-Universität zu Berlin, 2018. http://d-nb.info/1182540457/34.

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Schubert-Mielnik, Ulrich Verfasser], Wolfgang F. L. [Akademischer Betreuer] [Gutachter] Hollik, and A. [Gutachter] [Vairo. "Differential Equations and the Magnus Exponential for multi-loop multi-scale Feynman Integrals / Ulrich Schubert-Mielnik. Betreuer: Wolfgang F. L. Hollik. Gutachter: Antonio Vairo ; Wolfgang F. L. Hollik." München : Universitätsbibliothek der TU München, 2016. http://d-nb.info/1110014708/34.

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Primo, Amedeo. "Cutting Feynman Amplitudes: from Adaptive Integrand Decomposition to Differential Equations on Maximal Cut." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3426809.

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In this thesis we discuss, within the framework of the Standard Model (SM) of particle physics, advanced methods for the computation of scattering amplitudes at higher-order in perturbation theory. We offer a new insight into the role played by the unitarity of scattering amplitudes in the theoretical understanding and in the computational simplification of multi-loop calculations, at both the algebraic and the analytical level. On the algebraic side, generalized unitarity can be used, within the integrand reduction method, to express the integrand associated to a multi-loop amplitude as a su
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Torres, Bobadilla William Javier. "Generalised Unitarity, Integrand Decomposition, and Hidden properties of QCD Scattering Amplitudes in Dimensional Regularisation." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3423251.

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In this thesis, we present new developments for the analytic calculation of tree- and multi-loop level amplitudes. Similarly, we study and extend their analytic properties. We propose a Four-dimensional formulation (FDF) equivalent to the four-dimensional helicity scheme (FDH). In our formulation, particles propagating inside the loop are represented by four dimensional massive internal states regulating the divergences. We provide explicit four-dimensional representations of the polarisation and helicity states of the particles propagating in the loop. Within FDF, we use integrand reduc
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Sarkar, Ratan. "Asymptotic Analysis of Multi-scale, Multi-loop Feynman Diagrams." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5510.

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It is very challenging to solve multi-scale, multi-loop Feynman diagrams analytically. The presence of different kinematic scales makes the computation of Feynman diagrams very difficult, sometimes impossible to get the analytic results. One way to tackle this problem is to consider systematic approximations based on the hierarchies of the scales. The basic idea is to simplify the integral before the integration. The Method of Regions (MoR) is one of the powerful methods for handling the evaluation of multi-scale, multi-loop Feynman diagrams asymptotically. The whole loop momentum domain is d
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Book chapters on the topic "Multi-loop Feynman integrals"

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Marquard, Peter, and Matthias Steinhauser. "Numerical Evaluation of Multi-loop Feynman Integrals." In High Performance Computing in Science and Engineering ´16. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47066-5_8.

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Kurz, Alexander, Peter Marquard, and Matthias Steinhauser. "Numerical Evaluation of Multi-Loop Feynman Integrals." In High Performance Computing in Science and Engineering ´15. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-24633-8_2.

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Ananthanarayan, B., Abhishek Pal, Sunethra Ramanan, and Ratan Sarkar. "On the Determination of Regions in Multi-scale, Multi-loop Feynman Integrals." In Springer Proceedings in Physics. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-2354-8_36.

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Chaubey, Ekta. "Analytic Computation of Multi-loop Feynman Integrals for Higher-order QCD Corrections." In Springer Proceedings in Physics. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-0289-3_5.

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Tanasa, Adrian. "Quantum gravity, group field theory (GFT), and combinatorics." In Combinatorial Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895493.003.0010.

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This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, so
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Conference papers on the topic "Multi-loop Feynman integrals"

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Zhang, Yang, Janko Boehm, Dominik Bendle, et al. "Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals." In MathemAmplitudes 2019: Intersection Theory & Feynman Integrals. Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.383.0004.

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Chachamis, Grigorios, Sebastian Buchta, Petros Draggiotis, and Germán Rodrigo. "Attacking one-loop multi-leg Feynman integrals with the Loop-Tree Duality." In XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects. Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.265.0067.

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Meyer, Christoph. "Evaluating multi-loop Feynman integrals using differential equations: automatizing the transformation to a canonical basis." In Loops and Legs in Quantum Field Theory. Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.260.0028.

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You might also be interested in the extended bibliographies on the topic 'Multi-loop Feynman integrals' for particular source types:
Journal articles
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