Yang-Mills and the Foundations of Quantum Field Theory

Explore the mathematical foundations of Yang-Mills theories and their role in quantum field theory through this 55-minute Millennium Prize Problems lecture. Delve into how Yang-Mills theories form the building blocks of the Standard Model of quantum mechanics, which represents our best current understanding of the universe at the quantum scale, while examining why these theories lack rigorous mathematical foundations. Learn about the limitations of perturbation theory in physical calculations and discover phenomena believed to be beyond perturbative approaches. Understand the historical development of constructive field theory, a program initiated in the 1960s aimed at establishing mathematical rigor for these theories, and examine why this program has not yet achieved its original objectives despite numerous successes. Gain insight into the Clay Millennium Prize problem of Yang-Mills existence and mass gap, which seeks to complete this foundational work. Review the exciting recent progress made in the last decade that has reinvigorated efforts toward solving this fundamental problem in mathematical physics.