Advanced Lectures on Quantum Field Theory: Differential Equations for Feynman Integrals

14 Apr 2025, 13:00 → 15 Apr 2025, 17:00 Asia/Shanghai

1502 (四牌楼校区逸夫建筑馆丘成桐中心)

Christoph Dlapa (DESY)

Feynman integrals are of immense importance in high-energy and gravitational physics. Their evaluation is often the main bottleneck for improving the accuracy of theoretical predictions. In these lectures, we will first introduce the basic concepts needed to understand modern-day approaches for these computations. This includes different representations and regularizations, as well as integration-by-parts identities. We then derive the differential equations for a simple example and discuss in detail how they can be solved by transforming them to a canonical form. We then introduce several techniques for finding this canonical form and discuss their advantages and disadvantages. Finally, we show how these techniques can be generalized for cases involving elliptic integrals. In particular, we discuss how the relevant geometry underlying the integration problem can be identified.

Monday 14 April

13:30 → 15:00 Lecture 1: Feynman integrals: motivation, integral families, regularization, parametrization, IBPs

15:15 → 16:45 Lecture 2: Differential equations: derivation, blocks, canonical form, MPLs, pure functions, example of massless box, boundary constants

Tuesday 15 April

01:30 → 03:00 Lecture 3: Finding a canonical form: Lee's algorithm, CANONICA, leading singularities, Baikov representation

03:15 → 04:45 Lecture 4: Elliptic Feynman integrals: minimal solution, Picard-Fuchs operators and their factorization, canonical form, example of sunrise