Call in the Mathematicians — The Texas Scientist

Quantum field theory illustration — Credit: Simons Collaboration on Global Categorical Symmetries

When physicists want to explain how subatomic particles – such as electrons, photons, quarks and neutrinos – behave and interact, they use a framework called quantum field theory (QFT), a highly successful physical theory that helped predict the existence of the Higgs boson, antimatter and neutrinos.

But mathematicians view QFT, developed mostly by physicists, as incomplete. With an assist from math, they say, the physicists could start to know what makes quantum field theory work.

“Quantum field theory has many different facets, depending on where you’re standing, but we don’t yet know how to describe the whole thing.”

“It’s like the elephant in that classic children’s story,” said Dan Freed, a mathematician at UT Austin who has worked for much of his career at the interface between geometry and theoretical physics. “Quantum field theory has many different facets, depending on where you’re standing, but we don’t yet know how to describe the whole thing.”

Freed is part of a new international collaboration from the two disciplines that aims to get the math and physics on the same page about QFT through a new project funded by the Simons Foundation. If successful, their collaboration could bring physicists closer to solving some of their most vexing problems, like how to merge gravity and quantum mechanics into what Einstein, and every theoretical physicist since, considered the holy grail: quantum gravity. It might even lay the groundwork for completing the Final Theory, which would unify all the known forces in the universe. For mathematicians, QFT is a stimulating new playground of ideas from the physical world that could accelerate research in the more abstract realms they often inhabit.

“It’s a dialogue that impacts both fields,” Freed said.

Already experimental physicists are searching for undiscovered phases of matter predicted by a new class of mathematical theories called invertible QFTs that Freed and his colleagues recently developed and classified.