Related papers: On the thermodynamic limit of interacting fermions in the continuum

On the thermodynamic limit of interacting fermions in the continuum

URL: http://arxiv.org/abs/2409.10495v1
Date: Mon, 16 Sep 2024 17:27:50 GMT
Title: On the thermodynamic limit of interacting fermions in the continuum
Authors: Oliver Siebert,
Abstract summary: We study the dynamics of non-relativistic fermions in $mathbb Rd$ interacting through a pair potential. 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.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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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