Analytic integration methods in quantum field theory: an Introduction

Abstract

A survey is given on the present status of analytic calculation methods and the mathematical structures of zero-and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind.

The Principle of Global Relativity

“…Here also Higgsreducible diagrams contribute [23]. In these calculations special numbers like Cl(π/3) appear, that play a role in number theory, having connections with elliptic functions [24]. Altogether the effects were rather small.…”

Some examples of calculation of massless and massive Feynman integrals

“…Feynman integrals with massive propagators are significantly more complex objects compared to the massless case (see, for example, the recent review [29]). The basic rules for calculating such diagrams are discussed in Section 2, which are supplemented by new ones containing directly massive propagators.…”