Application and explicit solution of recurrence relations with respect to space-time dimension

2000/10/01 by O. V. Tarasov, O.V. Tarasov
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Appell series #Black Holes and Theoretical Physics #Dimension (graph theory) #Expression (computer science) #Feynman integral #Function (biology) #Generalized hypergeometric function #Hypergeometric function #Quantum Mechanics and Non-Hermitian Physics #Recurrence relation #Reduction (mathematics) #hep-ph

paper · pdf · doi:10.1016/s0920-5632(00)00849-5

published as Nucl.Phys.Proc.Suppl. 89 (2000) 237-245 · 9 pages, 1 figure, LaTeX

openalex publication_date 2000/10/01 · arxiv created 2001/02/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop integrals with arbitrary momenta and masses is presented. The result is written as multiple hypergeometric series depending on ratios of Gram determinants. For the 3-point function a new expression in terms of the Appell hypergeometric function F₁ is presented.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• One-loop tensor integrals in dimensional regularisation
• The gauge-Higgs system in three dimensions to two-loop order