 96676 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
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Dec 17, 96

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Abstract. We present a systematic description of the mathematical techniques for
studying multiloop Feynman diagrams which constitutes a fullfledged
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 socalled Euclidean asymptotic operation
for products of singular functions) is explicitly constructed
and studied.
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