English

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 Rd\mathbb R^d 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