When particle physicists try to model experiments, they confront an impossible calculation — an infinitely long equation that lies beyond the reach of modern mathematics. But three recent papers from a group of physicists led by Sebastian Mizera, Member in the School of Natural Sciences, and Pierpaolo Mastrolia of the University of Padua have revealed an underlying algebraic structure in the equations that provides a new way of collapsing interminable terms into just dozens of essential components.
Mastrolia and Mizera’s work is rooted in a branch of pure math called algebraic topology, which classifies shapes and spaces. Mathematicians pursue this classification with “cohomology” theories, which allow them to extract algebraic fingerprints from complicated geometric spaces.
“This is something that’s not just mathematics,” said quantum theorist Simon Caron-Huot, a past Long-term IAS Member who is studying the implications of Mizera and Mastrolia's work. “It’s something that’s deeply baked into quantum field theory.”
Read more at Quanta.