Feynman integrals and hyperlogarithms

Understand

We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions.

• Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals.
• This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly.
• Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals.