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$\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
- 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
- Subjects :
- Mathematical Physics
High Energy Physics - Theory
Subjects
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