Evaluation of arbitrary Feynman graphs via algorithmic methods.

Feynman diagrammatics is a powerful tool for the study of correlated electron systems. However, the formulation of diagrams in terms of Matsubara frequencies is not well suited to numerical computations due to an intrinsic inability to evaluate the unbounded Matsubara frequency integrals. In this talk we present an algorithm for fully symbolic evaluation of arbitrary Feynman diagrams that overcomes this issue, and many others. Further, from this perspective of analytics we identify a procedure for high order diagrams which allows for the optimal reduction of the sign problem. This is accomplished via invariant transformations that allow us to group diagrams whose integrands are analytically equal or analytically cancel.