96-676 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) 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 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.

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