Techniques of Distributions in Perturbative Quantum Field Theory (I) Euclidean asymptotic operation for products of singular functions

Kuznetsov, A. N.; Tkachov, F. V.; Vlasov, V. V.

Techniques of Distributions in Perturbative Quantum Field Theory (I) Euclidean asymptotic operation for products of singular functions

Authors

Kuznetsov, A. N.

Tkachov, F. V.

Vlasov, V. V.

Description

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.
87 pages, Latex-2.09