Zugl.: Regensburg, Univ., Diss., 2007.

Mainz, Univ., Diss., 2005. / Erscheinungsjahr an der Haupttitelstelle: 2004. Computerdatei im Fernzugriff.

Mainz, Univ., Diss., 2002. / Computerdatei im Fernzugriff.

Mainz, Univ., Diss., 2002. / Computerdatei im Fernzugriff.

Mainz, University, Diss., 2005. / Erscheinungsjahr an der Haupttitelstelle: 2004.

Mainz, University, Diss., 2005.

Mainz, Universiẗat, Diss., 2002.

This article aims to explain and justify the use of Feynmann diagrams as a computational tool in physics. The integrals discussed may be seen as a toybox version of the real physical case. It starts out with the basic one-dimensional Gaussian integral and then proceeds with examples of multidimensional cases. Correlators and their solutions through generating functions and Wick's theorem are shown, as well as some examples of how to relate the computations to diagrams and the corresponding rules for these diagrams.

Zugl.: Regensburg, Univ., Diss., 2007

We study the relations among unitarity cuts of a Feynman integral computed via diagrammatic cutting rules, the discontinuity across the corresponding branch cut, and the coproduct of the integral. For single unitarity cuts, these relations are familiar, and we show that they can be generalized to cuts in internal masses and sequences of cuts in different channels and/or internal masses. We develop techniques for computing the cuts of Feynman integrals in real kinematics. Using concrete one- and two-loop scalar integral examples we demonstrate that it is possible to reconstruct a Feynman integral from either single or double unitarity cuts. We then formulate a new set of complex kinematics cutting rules generalising the ones defined in real kinematics, which allows us to define and compute cuts of general one-loop graphs, with any number of cut propagators. With these rules, which are consistent with the complex kinematic cuts used in the framework of generalised unitarity, we can describe more of the analytic structure of Feynman diagrams. We use them to compute new results for maximal cuts of box diagrams with different mass configurations as well as the maximal cut of the massless pentagon. Finally, we construct a purely graphical coproduct of one-loop scalar Feynman diagrams. In this construction, the only ingredients are the diagram under consideration, the diagrams obtained by contracting some of its propagators, and the diagram itself with some of its propagators cut. Using our new definition of cut, we map the graphical coproduct to the coproduct acting on the functions Feynman diagrams and their cuts evaluate to. We finish by examining the consequences of the graphical coproduct in the study of discontinuities and differential equations of Feynman integrals.