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

Authors :
Aizawa, N.
Ito, Ren
Tanaka, Toshiya
Source :
AIMS Mathematics, 9 (2024) 10494-10510
Publication Year :
2024

Abstract

We present 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 is the first example of the quantum mechanical realization of an eight-dimensional irrep of the $\mathcal{N}=2$ $\mathbb{Z}_2^2$-supersymmetry algebra. The $\mathbb{Z}_2^2$-SQM is 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 are also investigated.<br />Comment: 16 pages, no figure

Details

Database :
arXiv
Journal :
AIMS Mathematics, 9 (2024) 10494-10510
Publication Type :
Report
Accession number :
edsarx.2401.02742
Document Type :
Working Paper
Full Text :
https://doi.org/10.3934/math.2024513