Connection between Feynman integrals having different values of the space-time dimension

1996/06/04 by O. V. Tarasov, O.V. Tarasov · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Particle physics theoretical and experimental studies #hep-ph #hep-th

paper · pdf · doi:10.1103/physrevd.54.6479

published as Phys.Rev. D54 (1996) 6479-6490 · 21 pages, LaTeX, uses axodraw.sty

arxiv created 1996/06/04 · openalex publication_date 1996/11/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals with respect to the space-time dimension d is proposed. The relation between d- and (d\ensuremath-2)-dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two-, and three-loop integrals. The new recurrence relations with respect to d are complementary to the recurrence relations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals can be naturally solved in the framework of the proposed generalized recurrence relations.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• A new approach to the Taylor expansion of multiloop Feynman diagrams

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