I will be the next AMA guest. So here it is a brief introduction of myself, and you can suggest some topic/questions that can be discussed during the session.
Academic Background. I obtained a master degree in theoretical physics almost ten years ago, working on the regularization of path integrals for supersymmetric QM models of particles in curved (Euclidean) background space. In particular, I focused on the mode regularization, both for the phase space and usual path integral, in N=1,2 SUSY sigma models. It has been a while, however, since I abandoned those topics.
Then, following the same cursus honorum as many others in my community, I shifted towards mathematics. My motivation was - and still is - that I don't like the sloppiness with which many subtle and interesting mathematical problems are dealt with in theoretical physics. I therefore did a Ph.D. in mathematics, with analysis and mathematical physics as main topics. During my Ph.D. I started working on the so-called mean field and classical limits of quantum (field) theories; i.e. on rigorously proving the emergence of classical/mean-field effective dynamics starting from the full quantum description of a given system. This is still my main area of research, but I also work in scattering theory (e.g. for Lindblad superoperators) and nonlinear partial differential equations of physical relevance.
Suggested topics. Below you can find a list of the topics on which it is more probable that I would have something meaningful to say, but feel free to ask anything else.
- Classical and mean field approximation of quantum systems (e.g. Bohr's correspondence principle; the emergence of Hartree, Gross-Pitaevskii, Vlasov, Hartree-Fock dynamics from many-body quantum systems; ...);
- The interplay between rigorous mathematical results and physics (e.g. Haag's theorem, the von Neumann measurement scheme, representation theory for the algebra of canonical commutation relations, ...);
- Partial Differential Equations "of evolution" (e.g. Schrödinger, Wave, Klein-Gordon, Dirac, ...);
- Mathematical foundations of quantum mechanics and quantum field theory;
- Quantization (from a mathematician's point of view).
In general, I think I could at least point to some references if you ask me questions about mathematical physics, apart from some topics on which I am quite ignorant (like e.g. all things related to homology/cohomology applied to physics, string theory, general relativity).
Also, even if I am not at all an expert, I like to read about logic, set theory, and in general the problems that arise in foundational mathematics. So this could also be a topic for a (very informal but interesting) discussion.
When and where. The AMA session will take place in the hbar chat room, the 12th of July at 16:00 UTC.