Multiloop Feynman Diagrams and Distribution Theory. Part 3: UV Renormalization inMomentum Space

摘要

UV renormalization of multiloop diagrams is studied using the techniques of theAs-operation developed in the precedent papers. A new representation of the Bogoliubov R-operation is obtained, which has the form of a substraction from the momentum space integrand of its asymptotic expansion at large integration momenta in the sense of the distribution theory. The substracted terms are obtained by applying to the integrand the As-operation with respect to all dimensional parameters (masses and external momenta) going at zero to an equal rate, and an additional renormalization (wherefrom the arbitrariness arises) of the logarithmically divergent term at the origin of the space of the integration momenta. It is shown that the class of substraction schemes thus defined contains the well known MS scheme of 't Hooft.