Title: Graph theory and Feynman integrals
| Speaker: | Paul Balduf |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: Feynman integrals are one of the most versatile tools in theoretical physics. They are used to compute perturbative solutions for various interacting systems. Examples include scattering amplitudes in quantum field theory, gravitational waves at black hole mergers, and the scaling behavior in statistical physics at critical points. Every Feynman integral is defined in terms of a corresponding Feynman graph, and besides the concrete physical application, it is interesting to study the number theory of Feynman integrals and how they are related to combinatorial properties of the underlying graph. What can we know about the value of the integral from examining the graph alone? In particular: Under which conditions will the Feynman integrals of two non-isomorphic graphs evaluate to the same number?
In addition to improved theoretical understanding, recent advances in algorithms and computational power have enabled a more numerical approach to these questions. This has led to the discovery of new qualitative features of Feynman integrals, such as correlations and empirical distribution functions. In my talk, I will discuss several results of this type for a model quantum field theory called $\phi^4$-theory. Some of these findings are highly useful for the efficient computation of physical quantities, while others give inspiration for a deeper conceptual understanding of Feynman integrals.
Joint work with Karen Yeats, Kimia Shaban, and Johannes Thürigen. My talk includes the necessary definitions of the Feynman integrals in question and does not require any background knowledge of physics.