Computer Algebra Methods in Probing the Physics at Shortest Distances of the Microcosm
The dynamics of the physics at the shortest probed distances in the microcosm are described by renormalizable Quantum Field Theories. The corresponding observables are given by large sets of Feynman parameter integrals. For quite a large series of important quantities their calculation can be performed analytically using computer-algebraic technologies, analytic methods from difference ring theory, the theory of differential equations and special functions and numbers. In course of these calculations multi Giga- to Tera terms are processed. A series of new related function space have been revealed in this way during the last years.
We describe these technologies as they stand, discuss further avenues, and present characteristic examples down to the associated numeric representations.