Feynman Integral Calculus

By Vladimir A. Smirnov. 2006

281 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9076774d5f7adf4343e77b6a5d84932e1a8f04ec

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Citations in the corpus

The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “[462], these reduce to products with ` = 1.”
Strong-coupling expansion of cusp anomaly from quantum superstring (2007, background): “(30)Such sunset diagram integrals in different dimensions were extensively discussed in the literature (see [42] and references therein) and can be found numerically, but their analytic form is apparently not known beyond few simple examples.”
An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM (2010, unknown): “[33, 34, 35, 36].”
Collider physics at the precision frontier (2020, methodology): “as been formulated by Laporta[433], therefore it is sometimes also called Laporta-algorithm. The public tools where this algorithm has been implemented will be listed in Section 3.1.4, see also Refs. [434, 435] for brief reviews of the method. Formulations of IBP reduction in terms of algebraic geom”
Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals (2010, methodology): “In fact, it has been elevated from a collection of loosely related prescriptions to a solid part of mathematical physics as was recently certified by the appearance of Smirnov’s bestseller books “Evaluating Feynman integrals” and (even!) “Feynman integral calculus” [2, 3].”
Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM (2011, methodology): “Finally we perform the Feynman parameter integration (see for example [49] for more details) to get”
Gravitational radiative corrections from effective field theory (2009, methodology): “(A6) Alternatively (and equivalently, using a well known integral representation for the hypergeometric function), one can introduce a Mellin-Barnes representation 1 (p+ l)(2) + (−k2 − iǫ) = ∫ i∞ −i∞ dz 2πi Γ(1 + z)Γ(−z) [(p+ l) (2)] z (−k2 − iǫ) , (A7) where the integration contour runs parallel to”
From correlation functions to scattering amplitudes (2010, methodology): “, [42]) using the package [43] for the ǫ-expansion and evaluation of the representations.”
FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS (2007, background): “D2 3D4 − 2 Z dDk1 (2π)D−2 dDk2 (2π)D−2 k · k2 D1D2D2 3D4 + −2 Z dDk1 (2π)D−2 dDk2 (2π)D−2 k · k2 D1D2 2D3D4 = 0 (21) Eq. (21) can be pictorially represented by − + + k2 + −2 (k · k2) − 2 (k · k2) = 0 (22) Feynman Diagrams & Diﬀerential Equations 11 where a dot on a propagator line means that the”