作为 N 体谐波振荡器系统的 $$\Phi ^4$$ 矩阵模型的可积分性

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Letters in Mathematical Physics Pub Date : 2024-03-25 DOI:10.1007/s11005-024-01783-2

Harald Grosse, Akifumi Sako

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引用次数: 0

摘要

我们研究了一个赫米提矩阵模型，其动力学项由 $ Tr (H\Phi ^2 )$ 给出，其中 H 是一个正定赫米提矩阵，与康采维奇矩阵模型类似，但其势能 $\Phi ^3$ 被 $\Phi ^4$ 取代。我们证明，它的分割函数求解了一个非相互作用 N 体谐振子系统的可积分薛定谔方程。

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Integrability of $ \Phi ^4$ matrix model as N-body harmonic oscillator system

We study a Hermitian matrix model with a kinetic term given by $ Tr (H \Phi ^2 )$, where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential $\Phi ^3$ replaced by $\Phi ^4$. We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system.

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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.