Singularitaetsstruktur der Zweipunktfunktion des freien Diracfeldes in einer globalen hyperbolischen Raumzeit

Motivated by the recent progress in our understanding of quantum field theories in a classical gravitational background due to the application of methods from microlocal analysis, we study the singularity structure of vector valued distributions. As a generalization of the wave front set we make use of the polarization set. For solutions of Dirac and Maxwell equations on arbitrary spacetimes the Dencker connection is shown to coincide with the usual spin- and Levi-Civita-connection respectively, implying that the strongest singularities propagate in a simple way. For the case of the Dirac equation we investigate applications in quantum field theory on curved spacetimes. Hadamard states of the free Dirac field are analyzed and it is shown that the wave front set of their two point functions is the same as in the scalar case. Furthermore we determine the polarization set and show that its form does not depend on the metric background. Finally, possible applications in renormalization theory are discussed. (orig.)40 refs.Available from TIB Hannover: RR 8919(1999-020) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman