Geodesic
Ternary $Z_3$-symmetric algebra and generalized quantum
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 102-123
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We present a generalized version of a quantum oscillator described by means of a ternary Heisenberg algebra. The model leads to a sixth-order Hamiltonian whose energy levels can be discretized using the Bohr–Sommerfeld quantization procedure. We note the similarity with the $Z_3$-extended version of Dirac's equation applied to quark color dynamics, which also leads to sixth-order field equations. The paper also contains a comprehensive guide to $Z_3$-graded structures, including ternary algebras, which form a mathematical basis for the proposed generalization. The symmetry properties of the model are also discussed.
Keywords: $Z_3$-graded algebraic structures, ternary algebras, cubic Heisenberg algebra, Bohr–Sommerfeld quantization, quantum oscillator. 
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R. Kerner. Ternary $Z_3$-symmetric algebra and generalized quantum. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 102-123. http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a6/

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