Mathematical problems in non-relativistic quantum electrodynamics

• Applicant: Professor Dr. Marcel Griesemer
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 531147062

This project addresses mathematical challenges from non-relativistic quantum electrodynamics (QED) of atoms (and molecules). Our investigations focus on the phenomenon of radiative decay and relaxation to the ground state of excited atoms. The excess energy in this process is emitted in the form of photons. Since photons are massless, the number of photons emitted can in principle be unlimited. This infrared problem is not expected to occur in the radiative decay of neutral atoms, but it is an open problem to prove it. We are attacking this problem from different directions using modern tools from the spectral and scattering theory of many-particle quantum systems. — Another problem we are working on concerns the regularity and the spatial exponential decay of bound states of an atom in QED. It is an open problem to extend well known ideas of Moser, Stampacchia, and Trudinger in the field of elliptic PDEs to QED, where the wave functions are vector-valued and associated with a finite range of energies, rather than a single eigenvalue.

• DFG Programme: Research Grants