This research proposal aims to explore the connections between motivic Galois theory and perturbative renormalization in quantum field theory, building on the work of Connes and Kreimer, and Connes and Marcolli. The project focuses on developing a refined Tannakian theory, establishing connections between Feynman periods and motives, and investigating motivic Galois symmetries for renormalization group flow.
Key findings
Establishes a comprehensive program to unify motivic Galois theory and quantum field theory.
Proposes new mathematical frameworks to understand renormalization through the cosmic Galois group.
Aims to develop algorithms for computing motivic properties of Feynman diagrams.
Limitations & open questions
The research is in its proposal stage and has not yet been conducted, thus findings and limitations are prospective.