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Mathematical Foundations of the Dimensional Method
Author(s) -
Rufa G.
Publication year - 1990
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19905020103
Subject(s) - uniqueness , scalar (mathematics) , set (abstract data type) , computer science , mathematics , calculus (dental) , mathematical analysis , geometry , medicine , dentistry , programming language
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 ϵ μνστ tensor in n dimensions and, related to this, the uniqueness of γ 5 . 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.