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arXiv · 2406.19103

A Novel Generalisation of Supersymmetry: Quantum $\mathbb{Z}_2^2$-Oscillators and their `superisation'

Andrew James Bruce
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Abstract

We propose a very simple toy model of a $\mathbb{Z}_2^2$-supersymmetric quantum system and show, via Klein's construction, how to understand the system as being an $N=2$ supersymmetric system with an extra $\mathbb{Z}_2^2$-grading. That is, the commutation/anticommutation rules are defined via the standard boson/fermion rules, but the system still has an underlying $\mathbb{Z}_2^2$-grading that needs to be taken into account.

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Andrew James Bruce. 2024-06-27. A Novel Generalisation of Supersymmetry: Quantum $\mathbb{Z}_2^2$-Oscillators and their `superisation'. https://doi.org/10.5506/aphyspolb.55.8-a1

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