Euclidean asymptotic expansions of Green functions of quantum fields (I) Expansions of products of singular functions

摘要

The problem of asymptotic expansions of Green functions in perturbative QFTis studied for the class of Euclidean asymptotic regimes. Phenomenologicalapplications are analyzed to obtain a meaningful mathematical formulation ofthe problem. It is shown that the problem reduces to studying asymptoticexpansions of products of a class of singular functions in the sense of thedistribution theory. Existence, uniqueness and explicit expressions for suchexpansions ("asymptotic operation for products of singular functions") indimensionally regularized form are obtained using the so-called extensionprinciple.