This paper introduces the parastatistics induced by ${\mathbb {Z}} _ {2}{\times}{\mathbb {Z}}
_ {2}-\mathrm {g}\mathrm {r}\mathrm {a}\mathrm {d}\mathrm {e}\mathrm {d} $ algebras. It …

A quantum mechanical model that realizes the Z 2× Z 2-graded generalization of the one-
dimensional supertranslation algebra is proposed. This model shares some features with …

In a previous paper we introduced the notion of Z 2× Z 2-graded classical mechanics and
presented a general framework to construct, in the Lagrangian setting, the worldline sigma …

Abstract Z _2 * Z _2 Z 2× Z 2-graded mechanics admits four types of particles: ordinary
bosons, two classes of fermions (fermions belonging to different classes commute among …

Machine learning systems are increasingly used to make decisions about people's lives,
such as whether to give someone a loan or whether to interview someone for a job. This has …

The superalgebra of ℤ 2 2-graded supersymmetric quantum mechanics is shown to be
realizable in terms of a single bosonic degree of freedom. Such an approach is directly …

In the recent paper (Bruce and Duplij 2019 (arXiv: 1904.06975 [math-ph])), Bruce and Duplij
introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an …

Irreducible representations (irreps) of Z 2 2-graded supersymmetry algebra of N= 2 are
obtained by the method of induced representation, and they are used to derive Z 2 2-graded …

We extend the notion of super-Minkowski space-time to include Z 2 n-graded (Majorana)
spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent …

A novel feature of the Z 2× Z 2-graded supersymmetry which finds no counterpart in ordinary
supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two …