Position Space Approach: Analyzing Banana Feynman Diagrams

This lecture discusses the position space approach to banana Feynman diagrams, focusing on the derivation of differential equations for Feynman integrals. The instructor begins with a review of multi-loop integrals and the complexities involved in their calculations. He introduces banana graphs and their connection to Calabi-Yau geometry, emphasizing the significance of the position space method. The lecture covers the integration by parts identities and how they can simplify the calculation of integrals. The instructor explains the role of differential equations in understanding Feynman integrals, particularly in the context of banana diagrams. He presents examples of how these equations can be derived and solved, highlighting the differences between equal and generic mass cases. The discussion extends to the implications of these findings for broader applications in quantum field theory and mathematical physics. The lecture concludes with insights into ongoing research and potential future directions in the study of Feynman diagrams and their geometric properties.