The characteristic Cauchy problem for Dirac fields on curved backgrounds
نویسندگان
چکیده
On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in L 2 and we give an explicit definition of the space of data on the light-cone producing a solution in H 1. The method is based on energy estimates following L. Hörmander [9].
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