On May 27, 2026, the "Nangao Shi · Physics Salon" lecture series, organized by the School of Physics and Technology at Nanjing Normal University, was held in Lecture Hall 436 of the Xingjian Building. Assistant Professor Wang Xing from The Chinese University of Hong Kong (Shenzhen) was invited to deliver an academic report titled "New Mathematical Structures in Feynman Integrals" to the faculty and students. The lecture was chaired by Associate Researcher Wang Yefan from the School of Physics and Technology, and was attended by several professors and graduate students from related disciplines.

During the report, Assistant Professor Wang Xing first reviewed the development of multi-loop Feynman integrals and introduced their wide applications in collider physics, formal theory, and gravitational wave physics. He pointed out that as the use of high-loop Feynman integrals becomes increasingly common in perturbative calculations, the study of Feynman integrals themselves has taken on significant mathematical and physical importance. After decades of development, the calculation of Feynman integrals has formed a set of systematic methods. However, obtaining analytical results for complex Feynman integrals remains a cutting-edge and exploratory problem.

Assistant Professor Wang then focused on the ε-factorization method. By applying a special treatment to the differential equations satisfied by Feynman integrals, the parameter ε related to the space-time dimension can be completely factored out, allowing iterative solutions of the relevant Feynman integrals. However, many loop integrals involving massive propagators are not directly amenable to ε-factorization, as these integrals contain not only well-studied polylogarithmic functions but also more complex mathematical structures such as elliptic integrals. To address this, Assistant Professor Wang and his collaborators developed a systematic method for constructing canonical differential equations. This method includes block-by-block processing of the differential equations, appropriate selection of master integrals, and systematic analysis based on the Baikov representation. Through a series of mathematical transformations and in-depth analysis of the mathematical structures of the integrals, they obtained an ordering of the complexity of the master integrals and successfully constructed canonical differential equations using the developed method. Finally, Assistant Professor Wang demonstrated several results achieved with this method and highlighted its advantages over traditional approaches, using concrete examples such as massless two-loop four-point planar diagrams and massive three-loop self-energy diagrams.

During the interactive session, the attending faculty and students engaged in in-depth exchanges and lively discussions with Assistant Professor Wang on related mathematical concepts, algorithmic implementations, and application scenarios. This report not only broadened the participants' understanding of Feynman integrals but also enriched their mathematical knowledge.

Biography of the Speaker:

Wang Xing is an Assistant Professor at the School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), and a recipient of the National High-Level Young Talents Program. He received his Bachelor of Science degree from Peking University in 2014 and his Ph.D. in Theoretical Physics from Peking University in 2019. From October 2019 to November 2024, he conducted postdoctoral research at Johannes Gutenberg University Mainz and the Technical University of Munich in Germany. At the end of 2024, he joined the School of Science and Engineering at CUHK-Shenzhen. His main research direction is perturbative quantum field theory and its applications in precise predictions for particle physics, while also exploring potential interdisciplinary connections with cosmology and mathematics.