New symmetries for modern physics 

Robert Moscrop will receive his doctoral degree in mathematics from Uppsala University in 2023. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will hold a postdoctoral position with Professor Michael Hopkins at Harvard University, Cambridge, USA. 

Mathematics and physics have a long history of developing through their symbiotic relationship. Mathematics provides the language necessary to describe physical phenomena, while physics pushes mathematics to introduce new ideas and methods when new discoveries are made. Symmetry is one of the cornerstones of this development. The classical perspective on symmetry can be understood as a transformation of one physical system to other, with the condition that the transformation does not change some measurable quantities. For example, if the charge of all particles changes sign from plus to minus, and this does not change the result of an experiment, there is symmetry in the system.   

In 1931, Eugene Wigner, who worked in the US, proved that to describe such classic symmetries, a previously known mathematical tool called group theory was necessary. Group theory was developed in the nineteenth century, but it was not until 100 years later that it proved invaluable in quantum field theory, a framework that unites the two new theories that revolutionised physics in the twentieth century – quantum physics and Einstein’s special theory of relativity. Wigner was awarded the Nobel Prize in 1963, for his work on applying group theory to quantum physics. Like many others, he was astounded by mathematics’ incredible ability to describe nature which, in a famous essay, he called “the unreasonable effectiveness of mathematics”. 

The concept of symmetry has recently been expanded to a new class of symmetries, relevant to quantum field theories, which are not captured by group theory. The purpose of the planned project is to further explore these new symmetries from the perspectives of both mathematics and physics, to better grasp the intricate structures of quantum field theory.