On the thermodynamic limit of interacting fermions in the continuum
Mathematical Physics
2025-03-26 v2 math.MP
Operator Algebras
Quantum Physics
Abstract
We study the dynamics of non-relativistic fermions in interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we identify an extension of the CAR algebra where the dynamics acts as a group of *-automorphisms, which are continuous in time in all sectors for fixed particle numbers. In addition, we identify a suitable dense subalgebra where the time evolution is also strongly continuous. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.
Keywords
Cite
@article{arxiv.2409.10495,
title = {On the thermodynamic limit of interacting fermions in the continuum},
author = {Oliver Siebert},
journal= {arXiv preprint arXiv:2409.10495},
year = {2025}
}
Comments
23 pages, v1->v2: fixed Lemma 5.2 and further minor changes, version accepted for publication in Lett. Math. Phys