Space–time dimensionality D as complex variable:Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D

摘要

We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable D (space–time dimensionality) provide a regular way to derive analytical representations of loop integrals. The representations derived have a form of exponentially converging sums. Several examples of the developed technique are given.