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arXiv · 2409.10495

On the thermodynamic limit of interacting fermions in the continuum

Oliver Siebert
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Abstract

We study the dynamics of non-relativistic fermions in $\mathbb R^d$ 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.

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Oliver Siebert. 2024-09-16. On the thermodynamic limit of interacting fermions in the continuum. https://doi.org/10.1007/s11005-025-01919-y

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