Christoph Dlapa 博士系列学术报告
Title: Advanced Lectures on Quantum Field Theory: Differential Equations for Feynman Integrals
Speaker: Christoph Dlapa
Affiliation: Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany (德国电子同步加速器中心)
Time:13:30 - 15:00, Monday, 14th April, 2025
15:15 - 16:45, Monday, 14th April, 2025
13:30 - 15:00, Tuesday, 15th April, 2025
15:15 - 16:45, Tuesday, 15th April, 2025
(UTC+8, Beijing Time)
Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing
（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Inviter: Zhengwen Liu（刘正文）
Lecture Introduction
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, 14th April, 2025 (2025年4月14日，周一)
● 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, 15th April, 2025 (2025年4月15日，周二)
● 13:30 → 15:00
Lecture 3: Finding a canonical form: Lee's algorithm, CANONICA, leading singularities, Baikov representation
● 15:15 → 16:45
Lecture 4: Elliptic Feynman integrals: minimal solution, Picard-Fuchs operators and their factorization, canonical form, example of sunrise
Speaker
Dr. Christoph Dlapa received his Bachelor's degree from Graz University of Technology in 2016, his Master's degree from ETH Zurich in 2018, and completed his PhD at the Max Planck Institute for Physics in 2021. Since then, he has been working as a postdoctoral fellow at DESY Hamburg. His research focuses on Feynman integrals, differential equations, and their applications in gravitational wave physics and collider physics.