UV Limit in Nonrelativistic QED

• Applicant: Professor Dr. Volker Bach
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 547264922

This proposal describes a mathematical research project that falls into the field of mathematical physics. The question proposed to study derives from models of quantum mechanics used in theoretical physics to describe the interaction of a single electron with the quantized radiation field, i.e., with photons. In spite of its seeming simplicity and many decades of research done on these models, numerous mathematical questions remain open, especially, the mathematical construction of the ultraviolet limit. It is proposed to study the ultraviolet limit for a simplified model, known as nonrelativstic QED or Pauli-Fierz model, in which the (relativistic) electron is replaced by a nonrelativistic particle that is minimally coupled to the photon field or by an even more simplified description. Furthermore, translation invariance plays an important role and the greater part of the project deals with quasifree photon states. As opposed to their relativistic counterparts, models of nonrelativstic QED right away define semibounded, self-adjoint linear operators on Hilbert spaces, which makes their mathematical analysis anemable to variational, functional analytic, and, in particular, spectral theoretic methods.

• DFG Programme: Research Grants
• International Connection: Mexico
• Cooperation Partner: Professor Dr. Miguel Ballesteros