Spectral theory of non-symmetric operators in time-dependent external fields and in globally hyperbolic spacetimes

• Applicant: Dr. Moritz Reintjes, Ph.D.
• Subject Area: Mathematics
• Term: from 2013 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 233673047

For the proposed research project, we plan to analyze non-symmetric operators defined on the space of solutions of the Dirac equation containing a time-dependent gravitational field. In more detail, we consider the Dirac equation defined on a globally hyperbolic spacetime background. The goal of this project is to develop a method for introducing a specific class of spectral projectors non-perturbatively, which have only been defined through a formal perturbation-expansion so far. In the case of a static spacetime those spectral projectors are supposed to be the well-known projectors on the negative (or positive) spectral subspaces of the relativistic hamilton operator. In order to develop this method step by step, we analyze the case of a closed Friedmann-Robertson-Walker (FRW) spacetime first.

• DFG Programme: Research Fellowships
• International Connection: Brazil, USA
• Host: Professorin Dr. Lydia Bieri