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

• URL: http://arxiv.org/abs/2406.19103v2
• Date: Wed, 7 Aug 2024 11:55:23 GMT
• Title: A Novel Generalisation of Supersymmetry: Quantum $\mathbb{Z}_2^2$-Oscillators and their `superisation'
• Authors: Andrew James Bruce,
• Abstract summary: We show how to understand the system as being an $N=2$ supersymmetric system with an extra $mathbbZ2$-grading. The commutation/anticommutation rules are defined via the standard boson/fermion rules, but the system still has an underlying $mathbbZ2$-grading.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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