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math-ph2025
The Dirac oscillator, generalised parastatistics and colour Lie superalgebras
Phillip S. Isaac, Mitchell Ryan
We study the Dirac oscillator in one, two and three spatial dimensions, showing that the corresponding ladder operators realise the -graded Lie su…
math-ph2024★ 7 cited
Graded colour Lie superalgebras for solving Lévy-Leblond equations
Mitchell Ryan
The Lévy-Leblond equation with free potential admits a symmetry algebra that is a -graded colour Lie superalgebra (see arXiv:1609.08224). We exten…
math-ph2024
Refining the grading of irreducible Lie colour algebra representations
Mitchell Ryan
We apply the loop module construction of arXiv:1504.05114 in the context of Lie colour algebras. We construct a bijection between the equivalence classes of all finite-dimensional…