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Feynman--Kac formula for the heat equation driven by fractional noise with Hurst parameter $H<1/2$ [PDF]
, 2012 In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter ...
Hu, Yaozhong, Lu, Fei, Nualart, David
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Reduction to master integrals via intersection numbers and polynomial expansions
Journal of High Energy Physics, 2023 Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly independent master ...
Gaia Fontana, Tiziano Peraro
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Conditional generalized analytic Feynman integrals and a generalized integral equation
International Journal of Mathematics and Mathematical Sciences, 2000 We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals.
Seung Jun Chang +2 more
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A Modified Analytic Function Space Feynman Integral and Its Applications
Journal of Function Spaces, 2014 We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances.
Seung Jun Chang +2 more
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A Feynman integral depending on two elliptic curves
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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Generalized transforms and convolutions
International Journal of Mathematics and Mathematical Sciences, 1997 In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product.
Timothy Huffman +2 more
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Reduze - Feynman Integral Reduction in C++ [PDF]
, 2010 Reduze is a computer program for reducing Feynman Integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the ...
't Hooft +14 more
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Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
Journal of High Energy Physics, 2017 We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the ...
Samuel Abreu +3 more
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From positive geometries to a coaction on hypergeometric functions
Journal of High Energy Physics, 2020 It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use intersection ...
Samuel Abreu +4 more
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Kira - A Feynman Integral Reduction Program [PDF]
, 2017 In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals.
Maierhoefer, Philipp +2 more
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