1996/12/03 by A. N. Kuznetsov, Alexey N. Kuznetsov∥, Kuznetsov, A. N. +6
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Mechanics and Applications #advanced mathematical theories #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9612037
87 pages, Latex-2.09
arxiv created 1996/12/03 · openalex publication_date 1996/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a systematic description of the mathematical techniques for studying multiloop Feynman diagrams which constitutes a full-fledged and inherently more powerful alternative to the BPHZ theory. The new techniques emerged as a formalization of the reasoning behind a recent series of record multiloop calculations in perturbative quantum field theory. It is based on a systematic use of the ideas and notions of the distribution theory. We identify the problem of asymptotic expansion of products of singular functions in the sense of distributions as a key problem of the theory of asymptotic expansions of multiloop Feynman diagrams. Its complete solution for the case of Euclidean Feynman diagrams (the so-called Euclidean asymptotic operation for products of singular functions) is explicitly constructed and studied.