The Number Theory of Quantum Equations of Motion

该奖项支持研究生参与研究微扰量子场论的李代数结构背后的数论性质。这项工作旨在有助于理解量子电动力学非凡的预测能力背后的数学。该项目的重点是对Dyson-Schwinger方程解中多个zeta值的出现进行了研究。这个研究项目补充了首席研究员对原始费曼图的动机性质的研究。可重整量子场论是目前对基本粒子相互作用最好的描述。尽管这一物理理论具有非凡的准确性和预测能力，但其潜在的数学公式仍然难以捉摸。这项工作继续了一项已经开始阐明量子场论的数学结构的研究。为这一物理理论发展适当的数学结构的进展可能导致理论的扩展和对基本粒子性质的更深入理解。

This award supports graduate student involvement in research on number-theoretic properties behind the Lie algebraic structure of perturbative quantum field theory. The work aims to contribute to the understanding of the mathematics behind the remarkable predictive power of quantum electrodynamics. The project is focused on an investigation into the appearance of multiple zeta values in solution of Dyson-Schwinger equations. This research program complements the principal investigator's investigation into the motivic nature of primitive Feynman graphs.brbrRenormalizable quantum field theory is currently the best available description of the interactions of elementary particles. Despite the remarkable accuracy and predictive power of this physical theory, its underlying mathematical formulation remains elusive. This work continues an investigation that has begun to elucidate the mathematical structure of quantum field theory. Advances in developing the proper mathematical structure for this physical theory could lead to extensions of the theory and deeper understanding of the nature of elementary particles.