A Feynman integral depending on two elliptic curves [PDF]
Journal of High Energy Physics, 2022 We study a two-loop four-point function with one internal mass. This Feynman integral is one of the simplest Feynman integrals depending on two elliptic curves. We transform the associated differential equation into an ε-form. We study the entries of the
Hildegard Müller, Stefan Weinzierl
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GKZ hypergeometric systems of the four-loop vacuum Feynman integrals [PDF]
Journal of High Energy PhysicsBasing on Mellin-Barnes representations and Miller’s transformation, we present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of 4-loop vacuum Feynman integrals with arbitrary masses. Through the GKZ hypergeometric systems, the analytical
Hai-Bin Zhang, Tai-Fu Feng
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One-loop Feynman integral reduction by differential operators [PDF]
Physical Review D, 2021 For loop integrals, the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman reduction. Inspired by the recent paper [1] where the tadpole reduction coefficients have been solved, in this paper we ...
Changwei Hu, Ting-Kai Li, Xiaodi Li
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The Maslov correction in the semiclassical Feynman integral [PDF]
Open Physics, 2011 The Maslov correction to the wave function is the jump of $$ \left( { - \frac{\pi } {2}} \right) $$ in the phase when the system passes through a caustic.
Horváthy Peter.
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Feynman Integral Relations from GKZ Hypergeometric Systems [PDF]
Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022), 2022 We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic scales.
Henrik J. Munch
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GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS [PDF]
, 2011 S. Chang, Jae Gil Choi, H. Chung
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Taming Calabi-Yau Feynman Integrals: The Four-Loop Equal-Mass Banana Integral. [PDF]
Physical Review Letters, 2022 Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how these integrals can be computed with the method of differential equations. The four-loop equal-mass banana integral is the simplest Feynman integral whose geometry is a
Sebastian Pögel +2 more
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Effects of water currents on fish migration through a Feynman-type path integral approach under $\sqrt{8/3}$ Liouville-like quantum gravity surfaces [PDF]
Theory in biosciences, 2021 A stochastic differential game theoretic model has been proposed to determine optimal behavior of a fish while migrating against water currents both in rivers and oceans. Then, a dynamic objective function is maximized subject to two stochastic dynamics,
Paramahansa Pramanik
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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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Bounded Collection of Feynman Integral Calabi-Yau Geometries. [PDF]
Physical Review Letters, 2018 We define the rigidity of a Feynman integral to be the smallest dimension over which it is nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a rigidity bounded by 2(L-1) at L loops provided they are in the class that we
J. Bourjaily +3 more
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