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
(158K, LaTeX)
ABSTRACT. 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.