Feynman Diagrams, Differential Reduction, and Hypergeometric Functions
arXiv:0901.4716
Abstract
We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this type of approach to the evaluation of Feynman diagrams is discussed.
7 pages, LaTeX, PoS style; based on a talk given by M.Kalmykov at ACAT 2008, Erice, Italy, Nov. 3-7, 2008; v2: few references added; v3: few references and some details added and conclusion is improved
References in corpus (5)
- On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
- Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
- Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
- Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation
- Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions
Cited by in corpus (8)
- HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
- HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
- Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
- Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
- Counting master integrals: integration by parts vs. differential reduction
- HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables
- Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation
- Counting master integrals: Integration by parts vs. functional equations