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.
Renormalizable 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.
