$ \mathcal{N} = 2 $ double graded supersymmetric quantum mechanics via dimensional reduction

IF 1.8 3区 数学 Q1 MATHEMATICS
N. Aizawa, Ren Ito, Toshiya Tanaka
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引用次数: 0

Abstract

We presented a novel $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $-graded supersymmetric quantum mechanics ($ {\mathbb{Z}_2^2} $-SQM) which has different features from those introduced so far. It is a two-dimensional (two-particle) system and was the first example of the quantum mechanical realization of an eight-dimensional irreducible representation (irrep) of the $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $-supersymmetry algebra. The $ {\mathbb{Z}_2^2} $-SQM was obtained by quantizing the one-dimensional classical system derived by dimensional reduction from the two-dimensional $ {\mathbb{Z}_2^2} $-supersymmetric Lagrangian of $ \mathcal{N} = 1 $, which we constructed in our previous work. The ground states of the $ {\mathbb{Z}_2^2} $-SQM were also investigated.
$ \mathcal{N} = 2 $ 通过降维的双梯度超对称量子力学
我们提出了一个新颖的 $ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $ 等级超对称量子力学($ {\mathbb{Z}_2^2} $-SQM),它具有与迄今为止提出的量子力学不同的特征。它是一个二维(两粒子)系统,是$ \mathcal{N} = 2 $ $ \mathbb{Z}_2^2 $超对称代数的八维不可还原表示(irrep)的量子力学实现的第一个例子。$ {\mathbb{Z}_2^2} $-SQM是通过量子化二维 $ {\mathbb{Z}_2^2} $ \mathcal{N} = 1 $超对称拉格朗日的一维经典系统而得到的。我们还研究了 $ {\mathbb{Z}_2^2} $-SQM 的基态。
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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