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

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.

6 pages, accepted for publication in Acta Physica Polonica B

Cited by in corpus (1)

• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra