A Higher Spin Statistics Theorem for Invertible Quantum Field Theories

Abstract: The spin-statistics theorem asserts that in a unitary quantum field theory, the spin of a particle—characterized by its transformation under the central element of the spin group, which corresponds to a 360-degree rotation—determines whether it obeys bosonic or fermionic statistics. This relationship can be formalized mathematically as equivariance for a geometric and algebraic action of the 2-group ${\rm B}{\bf Z}_2$. In my talk, I will present a refinement of these actions, extending from ${\rm B}{\bf Z}_2$ to appropriate actions of the stable orthogonal group ${\rm O}$, and demonstrate that every unitary invertible quantum field theory intertwines these ${\rm O}$-actions.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)