Abstract. We give a non-perturbative construction of the fermionic projector in Minkowski space coupled to a time-dependent external potential which is smooth and decays faster than quadratically for large times. The weak and strong mass oscillation properties are proven. We show that the integral kernel of the fermionic projector is of Hadamard form, provided that the time integral of the spatial supnorm of the potential satisfies a suitable bound. This gives rise to an algebraic quantum field theory of Dirac fields in an external potential with a distinguished pure quasi-free Hadamard state.
An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The threedimensional field structure close to the heliopause is calculated as a solution of the induction equation under the assumption that it is frozen into a prescribed plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. The usefulness of this analytical solution as an approximation to self-consistent magnetic field configurations obtained numerically from the full MHD equations is illustrated by quantitative comparisons.
We consider a boundary value problem for the Dirac equation in a 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 spacetime includes horizons, where the Hamiltonian fails to be elliptic.
We suggest that large radiative corrections appearing in the spinfoam framework might be tied to the implicit sum over orientations. Specifically, we show that in a suitably simplified context the characteristic "spike" divergence of the Ponzano-Regge model disappears when restricting the theory to just one of the two orientations appearing in the asymptotic limit of the vertex amplitude.
We construct a SU (2) connection formulation of Kerr isolated horizons. As in the non-rotating case, the model is based on a SU (2) Chern-Simons theory describing the degrees of freedom on the horizon. The presence of a non-vanishing angular momentum modifies the admissibility conditions for spin network states. Physical states of the system are in correspondence with open intertwiners with total spin matching the angular momentum of the spacetime.PACS numbers: * Unité Mixte de Recherche (UMR 6207) du CNRS et Aix-Marseille Université; laboratoire affiliéà la FRUMAM (FR 2291).
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