20.02.2025, 10:15
– Raum 0.12 in Haus 9
Forschungsseminar Differentialgeometrie
Kähler and quaternion-Kähler manifolds of non-negative curvature
Uwe Semmelmann (Stuttgart)
Max Lewandowski
In the case of the Klein-Gordon field on Minkowski space a certain linear combination of the 4 standard fundamental solutions (advanced, retarded, Feynman and anti-Feynman propagator) yields a Hadamard state. Inspired by the construction of the advanced and retarded fundamental solutions on globally hyperbolic spacetimes for normally hyperbolic operators acting on sections in some vector bundle, a sketch of the corresponding construction for the Feynman and anti-Feynman propagator by a Hadamard series will be given. We will see that for the operator being formally self-adjoint the corresponding Hadamard coefficients turn out to have a certain symmetry property leading to the right antisymmetric part of the corresponding linear combination of fundamental solutions in the general setting, i.e. that of a Hadamard state.