On the thermodynamic limit of interacting fermions in the continuum

IF 1.4 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Letters in Mathematical Physics Pub Date : 2025-03-21 DOI:10.1007/s11005-025-01919-y

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 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 \(C^*\)-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.

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连续介质中费米子相互作用的热力学极限

我们研究了\(\mathbb {R}^d\)中非相对论费米子通过对势相互作用的动力学。采用Buchholz在可解代数框架中开发的方法，我们考虑了CAR代数的扩展，其中动力学作为一组\(*\) -自同构，这些自同构在所有扇区对固定粒子数在时间上连续。此外，我们通过识别合适的密集子代数构造了一个\(C^*\) -动力系统。最后，我们简要讨论了未来如何使用该框架来构建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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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.

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