On Maxwell's equations on globally hyperbolic spacetimes with timelike boundary
Nicolò Drago (Universität Würzburg)
Abstract: 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 $\Box_k$ 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 $\delta d$. First we introduce two distinguished boundary conditions, dubbed $\delta d$-tangential and $\delta d$-normal boundary conditions. Associated to these we introduce two different notions of gauge equivalence for the solutions of the Maxwell's operator and we prove that in both cases, every equivalence class admits a representative abiding to the Lorentz gauge. We then construct a unital $*$-algebras $\mathcal{A}$ 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, $\mathcal{A}$ possesses a non-trivial center.
mathematical physicsanalysis of PDEsspectral theory
Audience: researchers in the topic
Scattering, microlocal analysis and renormalisation
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Links to the slides can be found here: drive.google.com/file/d/1uu6ZvU6zlGalJpZR7ZDi7igsvBMBylOA/view
Organizers: | Claudio Dappiaggi, Jacob Schach Møller, Michał Wrochna* |
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