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Self-adjointness of the Dirac Hamiltonian for a class of non-uniformly elliptic boundary value problems

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Finster, Felix ; Röken, Christian
Date of publication of this fulltext: 17 Dec 2015 08:21


We consider a boundary value problem for the Dirac equation in a four-dimensional, smooth, asymptotically flat Lorentzian manifold admitting a Killing field which is timelike near and tangential to the boundary. A self-adjoint extension of the Dirac Hamiltonian is constructed. Our results also apply to the situation that the space-time includes horizons, where the Hamiltonian fails to be elliptic.

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