Quantum Field Theory on Low-Regularity Spacetimes

Explore quantum field theory on low-regularity spacetimes in this 43-minute conference talk from the Workshop on "Non-regular Spacetime Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the mathematical foundations required to describe observables for quantum fields on spacetimes with reduced regularity, focusing on a massless scalar field on a globally hyperbolic spacetime with a C1,1 metric. Examine the well-posedness of the classical Cauchy problem for the wave equation, the construction of low-regularity Green operators, and the definition of appropriate function spaces. Learn how the causal propagator is used to define a symplectic form, enabling a locally covariant description of quantum fields using quasi-local C*-algebras. Investigate the definition of physical states in the low-regularity setting, particularly adiabatic states defined by the Sobolev wavefront set of the two-point function.