Using functional equations to calculate Feynman integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 324-342
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We propose a method for using functional equations to calculate Feynman integrals analytically. We describe the algorithm for solving the functional equations and show that a solution of a functional equation for the Feynman integral is a combination of several integrals with fewer kinematic variables. In some cases, using the functional equations, we can also reduce these integrals to integrals with even fewer variables. Such a stepwise application of the functional equations leads to integrals that can be calculated more simply than the original integral. We apply the proposed method to several one-loop integrals. For the three-point and four-point integrals with massless propagators and an arbitrary space dimension $d$, we obtain analytic expressions in terms of hypergeometric functions.
Keywords:
Feynman integral, functional equation, hypergeometric function.
@article{TMF_2019_200_2_a11,
author = {O. V. Tarasov},
title = {Using functional equations to calculate {Feynman} integrals},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {324--342},
publisher = {mathdoc},
volume = {200},
number = {2},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a11/}
}
O. V. Tarasov. Using functional equations to calculate Feynman integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 324-342. http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a11/