Mathematical Foundations of the Dimensional Method

We summarize and discuss important mathematical foundations concerning the dimensional method. To this end we carefully discuss the assumptions as well as the derived fundamental statements. We define and investigate the uniqueness of the ϵμνστ tensor in n dimensions and, related to this, the uniqueness of γ5. Furthermore, we develop an algorithm which allows the calculation of a set of scalar multi-loop integrals with masses in a systematic way. To demonstrate and test the algorithm we rederive a set of scalar integrals which are important in calculations at the one and two loop level. Mathematische Grundlagen der Dimensionalen Methode Wichtige mathematische Grundlagen der Dimensionalen Me…