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- Title
Ternary -symmetric algebra and generalized quantum oscillators.
- Authors
Kerner, R.
- Abstract
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 -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 -graded structures, including ternary algebras, which form a mathematical basis for the proposed generalization. The symmetry properties of the model are also discussed.
- Subjects
ALGEBRA; DIRAC equation; MATHEMATICAL forms; GEOMETRIC quantization
- Publication
Theoretical & Mathematical Physics, 2024, Vol 218, Issue 1, p87
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577924010070