SECTOR DECOMPOSITION

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multiloop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.

EXTRACTION OF INFRARED DIVERGENCES IN THE DIMENSIONAL REGULARIZED TWO-LOOP LADDER GRAPH

We consider the evaluation of the fundamental scalar integral in the on-shell two-loop ladder graph with different external masses and arbitrary transfer momentum. A method for cleanly extracting the infrared divergences in the Feynman parameter integrals using dimensional regularization is presented, and we analyze one of the finite part contributions to this integral.

NEW METHOD OF MASSIVE FEYNMAN DIAGRAMS CALCULATION

A new method of massive Feynman integrals calculation which is based on the rule of integration by parts is presented. This rule is expanded to the massive case. By applying this rule, we obtain a differential equation with respect to the mass for the initial diagram. The right-hand side of the equation contains simpler diagrams (i.e., containing only loops, not chains). This can be done by applying the procedure consecutively. These loops can be calculated either by the standard Feynman-parameter procedure or by a procedure which decreases the number of loops step-by-step. We demonstrate the capacities of this method for various complicated diagrams and make an attempt to analyze other possible massive Feynman diagrams calculations.

Fredholm Approximations in the Scalar Bethe-Salpeter Equation

The Fredholm approximation is discussed in the framework of the scalar Bethe-Salpeter equation. The trace of the angular momentum decomposed kernel is expressed in terms of Feynman parameter integrals which shows the relation to the vertex function. A new derivation for this representation is given which is far more direct than the previous one. Using this representation, several general features of the eigenvalues are discussed. For special cases, the trace is computed explicitly, and the numerical values are compared with the exact ones, obtained by variational methods.