2003/03/31 by A. P. Isaev, A.P. Isaev · 3 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Quantum and Classical Electrodynamics #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/s0550-3213(03)00393-6
published as Nucl.Phys. B662 (2003) 461-475 · 15 pages, Latex, corrected some typos and list of Refs
openalex publication_date 2003/06/02 · arxiv created 2003/06/05 · arxiv updated 2010/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless ϕ3 theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the ϕ3 scalar field theory are given by the Green function for the conformal quantum mechanics.