Periods and Hodge structures in perturbative quantum field theory
Stefan Weinzierl
TL;DR
This paper explores the deep connections between algebraic geometry and perturbative quantum field theory, focusing on periods, Hodge structures, and Picard-Fuchs equations and their relation to Feynman integrals.
Contribution
It reviews key mathematical concepts and discusses their relevance to understanding Feynman integrals in quantum field theory.
Findings
Highlights the role of algebraic geometry in quantum field theory
Connects periods and Hodge structures to Feynman integrals
Discusses Picard-Fuchs equations in the context of quantum calculations
Abstract
There is a fruitful interplay between algebraic geometry on the one side and perturbative quantum field theory on the other side. I review the main relevant mathematical concepts of periods, Hodge structures and Picard-Fuchs equations and discuss the connection with Feynman integrals.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · History and Theory of Mathematics · Black Holes and Theoretical Physics