We study Maxwell's equations as a theory for smooth k-forms on globally hyperbolic spacetimes with a timelike boundary. For that, we investigate the wave operator ◻k with appropriate boundary conditions and characterize the space of solutions of the associated initial and boundary value problem under reasonable assumptions. Subsequently we focus on the Maxwell operator δd. First we introduce two distinguished boundary conditions, dubbed δd -tangential and δd -normal boundary conditions. Associated to these we introduce two different notions of gauge equivalence for the solutions of the Maxwell's operator δd and we prove that in both cases, every equivalence class admits a representative abiding to the Lorentz gauge. We then construct a unital -algebra A of observables for the system described by the Maxwell's operator. Finally we prove that, as in the case of the Maxwell operator on globally hyperbolic spacetimes with empty boundary, A possesses a non-trivial center.
This talk is part of series of talks affiliated with the virtual Mittag-Leffler workshop "Scattering, microlocal analysis and renormalization", organized by Claudio Dappiaggi, Jacob Schach Møller and Michal Wrochna. The full schedule can be found at: