On the thermodynamic limit of interacting fermions in the continuum

arXiv - MATH - Operator Algebras Pub Date : 2024-09-16 DOI:arxiv-2409.10495

Oliver Siebert

引用次数: 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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论连续体中相互作用费米子的热力学极限

我们研究了$\mathbb R^d$中通过一对势相互作用的非相对论费米子的动力学。利用布霍尔茨（Buchholz）在解析代数框架内开发的方法，我们确定了CAR代数的一个扩展，在这个扩展中，动力学作为一个*-自变量组，对于固定粒子数，在所有扇区中都是时间连续的。此外，我们还确定了一个合适的稠密子代数，其中的时间演化也是强连续的。最后，我们简要讨论了未来如何利用这一框架来构建KMS状态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Operator Algebras

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