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 …

We present an algorithmic classification of the irreps of the N-extended one-dimensional
supersymmetry algebra linearly realized on a finite number of fields. Our work is based on …

It is shown that the N= 1 supersymmetric quantum mechanics (SQM) can be extended to a Z
2 n-graded superalgebra. This is done by presenting quantum mechanical models that …

It is a curious fact that our most well-studied BSM theories can inform us about the Standard
Model itself. Just over a decade ago,[1], Baez and Huerta explained how the Standard …

Quantum mechanical systems whose symmetry is given by $\mathbb {Z} _2^ 3$-graded
version of superconformal algebra are introduced. This is done by finding a realization of a …

It is shown that a simple continuity condition in the algebra of split octonions suffices to
formulate a system of differential equations that are equivalent to the standard Dirac …

An optimal algebraic model of particle physics has a number of checkpoints to pass. As a
minimum, models should $\langle 1\rangle $ conform to the Coleman-Mandula theorem (or …

A bstract A classification of spinor fields according to the associated bilinear covariants is
constructed in arbitrary dimensions and metric signatures, generalizing Lounesto's 4D …

Real Clifford algebras for arbitrary numbers of space and time dimensions as well as their
representations in terms of spinors are reviewed and discussed. The Clifford algebras are …

We extend vector formalism by including it in the algebra of split octonions, which we treat as
the universal algebra to describe physical signals. The new geometrical interpretation of the …