Fermionic integrable models and graded Borchers triples

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Letters in Mathematical Physics Pub Date : 2024-11-06 DOI:10.1007/s11005-024-01865-1
Henning Bostelmann, Daniela Cadamuro
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Abstract

We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1-dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, although it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag–Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme.

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费米子可积分模型和梯度博尔赫斯三元组
我们为 1+1 维明考斯基空间上具有费米子散射态的量子场论可积分模型提供了一种算子代数构造。这些模型是通过对楔局部场进行分级,或者对定义理论的底层博尔赫斯三重场进行分级而得到的。这就产生了一个分级局域场代数网,其中的偶数部分可以被认为是可观测的,尽管它缺乏哈格对偶性。重要的是,意味着局部场代数非琐碎性的核性条件与分级无关,因此可以利用关于这一技术问题的现有结果。哈格-鲁尔散射理论的应用证实渐近粒子确实是费米子粒子。我们还讨论了与形式因子方案的联系。
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来源期刊
Letters in Mathematical Physics
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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