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Speaker:
Christian Bär
Zugehörigkeit:
Potsdam
Datum:
Don, 16/04/2015 - 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Oberseminar Differentialgeometrie We prove an index theorem for the Dirac operator on compact Lorentzian manifolds with spacelike boundary. Unlike in the Riemannian situation, the Dirac operator is not elliptic. But it turns out that under Atiyah-Patodi-Singer boundary conditions, the kernel is finite dimensional and consists of smooth sections. The corresponding index can be expressed by a curvature integral, a boundary transgression integral and the eta-invariant of the boundary just as in the Riemannian case. There is a natural physical interpretation in terms of particle-antiparticle creation. This is joint work with Alexander Strohmaier.
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