Spectral analysis of mathematical models in quantum field theory

• Applicant: Professor Dr. Walter Aschbacher
• Subject Area: Mathematics
• Term: from 2009 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 162961698

In recent years, powerful methods have been developed for the rigorous treatment of mathematical models in semi-relativistic quantum electrodynamics. But it turns out that these methods also successfully apply to the description of processes in fully relativistic quantum field theory beyond quantum electrodynamics. In the present project, we want to extend and develop the high potential of these methods in order to cover the mathematical study of processes in a wide range of different model classes. As an example of such a process, we study the spectral theory of the decay of the negatively charged intermediate vector boson of the weak nuclear interaction into an electron and an electron antineutrino. Under physically sensible assumptions, we aim at determining the spectral nature of the interacting system what eventually leads to the construction of its scattering theory. The project thus contributes to a deeper understanding of important mathematical aspects of the Standard Model of elementary particle physics which unifies the electromagnetic, the weak nuclear, and the strong nuclear interaction in a single quantum theory.

• DFG Programme: Research Fellowships
• International Connection: France
• Host: Professor Dr. Jean-Claude Guillot