Self-interacting Path Measures

• Applicant: Professor Dr. Volker Betz
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 535662048

Path measures with self-interaction are first of all a probabilistic model, where well-known stochastic processes are perturbed by a self-interaction potential. However, they also have a close connection to models of a quantized field interacting with a quantized particle. For one of these models, the Fröhlich polaron, spectacular progress has been achieved in the last few years about the long open question of the effective mass. Part of this progress comes from probabilistic methods, another part from analytic ones. The new probabilistic methods are very recent (some less than a year old) but have turned out to be extremely powerful for the Fröhlich polaron. In this project, they shall be extended and refined, in order to apply them to similar models where they at the moment cannot be applied yet, and to get similarly strong results also in these models. Apart from that, in both the areas of probability and functional analysis there are strong groups working on problems that originate from the same or very similar quantum models. They however use very different methods, and there is little direct interaction. An important aim of this project is to help to bridge that gap and to bring these to groups closer together. The PI is well positioned to do this, being part of the probabilistic group, but with a decent background in mathematical physics, and good connections to some members of the analytic group investigating the interaction of quantum fields and matter.

• DFG Programme: Research Grants
• International Connection: Austria, USA
• Cooperation Partners: Dr. David Mitrouskas; Professor Dr. Mark Sellke
• Co-Investigator: Dr. Benjamin Hinrichs