On the thermodynamic limit of interacting fermions in the continuum

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2025年3月21日

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Oliver Siebert

摘要

We study the dynamics of non-relativistic fermions in $\mathbb {R}^d$ $R^{d}$ interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we consider 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 construct a $C^*$ $C^{*}$ -dynamical system by identifying a suitable dense subalgebra. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.