Speaker: David O'Connell (Okinawa Institute of Science and Technology)

Title: Colimits of C*-algebras in Quantum Field Theory

Time/Date: 1:00-2:30pm, February 21 (Fri.), 2025

Room: 002 Math Sci Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: In the formalism of locally-covariant quantum field theory one assigns a C* algebra to each globally hyperbolic spacetime, so as to generalize the approach of algebraic QFT to curved spaces. This assignment is functorial by construction, so that a quantum field theory is defined to be a functor from some appropriate category of spacetimes to some category of C* algebras. In this talk we will study the potential extension of this formalism to include colimits of a particular type. On the spacetime side, we will consider colimits of spacetimes known as "non-Hausdorff spacetimes", and on the algebraic side we will determine their associated C* algebras as particular amalgamated products. We will see that there are subtleties with this assignment: naive colimits of C*-algebras (despite existing) will not be the best choice physically, since they violate some desirable properties of algebraic QFT. We will discuss how to fix this issue, and then we will explain this result in relation to the Klein-Gordon field computed on a non-Hausdorff background.