Quantum Field Theory on low-regularity spacetimes

James A. Vickers (U Southampton)

Mar 17. 2023, 11:00 — 11:45

In this talk  I will describe the mathematics required in order to provide a description of the observables for quantum fields on low-regularity spacetimes. In particular we consider the case of a massless scalar field ϕ on a globally hyperbolic spacetime M with C1,1 metric g. This first entails showing that the (classical) Cauchy problem for the wave equation is well-posed for initial data and sources in Sobolev spaces and then constructing low-regularity advanced and retarded Green operators as maps between suitable function spaces. In specifying the relevant function spaces we need to control the norms of both ϕ and □gϕ in order to ensure that □gG± and G±◦□g are the identity maps on those spaces. The causal propagator G = G+ − G− is then used to define a symplectic form ω on a normed space V(M) which is shown to be isomorphic to ker(□g). This enables one to provide a locally covariant description of the quantum fields in terms of the elements of quasi-local C*-algebras. In the second half of the talk I will examine the definition of the physical states states in the low-regularity setting. These are the so-called adiabatic states which are defined in terms of the Sobolev wavefront set of the two point funtion. 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Non-regular Spacetime Geometry (Workshop)
Organizer(s):
Piotr T. Chruściel (U of Vienna)
Melanie Graf (U Hamburg)
Michael Kunzinger (U of Vienna)
Ettore Minguzzi (U Florence)
Roland Steinbauer (U of Vienna)