A new approach to physical solutions of scalar wave equations on globally hyperbolic Lorentzian manifolds

10.12.2015, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 1.11
Forschungsseminar Differentialgeometrie

Max Lewandowski

After Radzikowski's celebrated equivalence theorem in the 1990's microlocal analysis and especially the wave front set of solutions of wave equations on globally hyperbolic Lorentzian manifolds experienced growing interest in the QFT on CST society. For solutions of the Klein Gordon equation he proved that their particular singularity structure on the light cone is equivalent to a certain condition on their wave front set. In my talk I will consider scalar solutions of d'Alembert's equation on Minkowski space which for microlocal reasons yield the same singularity structure as scalar solutions of general wave equations on Lorentzian manifolds. Instead of starting with Wightman's axioms I will present another approach finding appropriate solutions involving Riesz distributions and distributional regularization instead and in the end show that they coincide with those "physical solutions" Radzikowski's Theorem is aimed at.