Understanding quantum field theory and the universe
Quantum field theories give the most precise descriptions known of the fundamental particles that make up the universe. However, they are difficult to understand partly because their mathematical structure is subtle.
As Canada Research Chair in Combinatorics in Quantum Field Theory, Karen Yeats seeks to understand quantum field theory using a combinatorial aesthetic and toolbox. Yeats’ research will look at Feynman diagrams in terms of their graph theory. Feynman diagrams are pictures that show how particles can interact.
Because, to understand quantum field theory we need to understand not just individual Feynman diagrams but the series consisting of all possible diagrams with a given beginning and end. Her research examines these series expansions in quantum field theory as connective generating functions.
This approach is rich and powerful. It will yield results that are interesting both as pure mathematics and as mathematical physics.
Yeats’ research will provide new approaches for understanding Feynman integrals and how they are put together into the series which calculate physical observables. This, in turn, has the potential to lead to significant advances in how we understand the building blocks that make up our universe.