Kuznetsov A.N., Tkachov F.V.
TECHNIQUES OF DISTRIBUTIONS IN PERTURBATIVE QUANTUM FIELD THEORY
(II) Applications to Theory of Multiloop Diagrams.
(107K, LaTeX)
ABSTRACT. The results of the mathematical theory of asymptotic operation developed
in [I] are applied to problems of immediate physical interest.
First, the problem of UV renormalizationis analyzed from the viewpoint
of asymptotic behaviour of integrands in momentum representation.
A new prescription for UV renormalization in momentum space representation
is presented (generalized minimal subtraction scheme);
it ensures UV convergence of renormalized diagrams by construction,
makes no use of special (e.g. dimensional) regularizations,
and comprizes massless renormalization schemes (including the MS scheme).
Then we present formal regularization-independent
proofs of general formulae for Euclidean asymptotic expansions of renormalized
Feynman diagrams (inlcuding short-distance OPE, heavy mass expansions and
mixed asymptotic regimes etc.) derived earlier in the context
of dimensional regularization. This result, together with the new variant
of UV renormalization, demonstrates the power of the new
techniques based on a systematic use of the theory of distributions and
establishes the method of As-operation as a comprehensive
full-fledged---and inherently more powerful---alternative
to the BPHZ approach.