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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.08978 |
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| _version_ | 1866908968499019776 |
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| author | Boumali, Abdelmalek Garrah, Sarra |
| author_facet | Boumali, Abdelmalek Garrah, Sarra |
| contents | We formulate the Dirac oscillator covariantly in the presence of external non-Abelian gauge fields. More precisely, the matter field is written as $Ψ_{αA}(x)$, where $α$ denotes the Dirac index and $A$ the isospin index, so that the Hamiltonian acts on the tensor-product space $\mathbb{C}^{4}\otimes\mathbb{C}^{2}$ in the fundamental representation. Starting from the gauge-covariant Dirac equation, we then implement the oscillator interaction through the standard non-minimal substitution and promote the construction to an $\mathrm{SU}(2)$ background. In this way, we derive the associated non-Abelian field-strength tensor and isolate the commutator contribution, which has no Abelian analogue. Consequently, the generalized Pauli interaction $σ^{μν}\mathcal{F}_{μν}$ produces matrix-valued spin--isospin couplings. At the same time, the Abelian sector reduces to the conventional Moshinsky--Szczepaniak Dirac oscillator, whose exactly solvable spectrum provides a natural benchmark for the extended theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Abelian Extensions of the Dirac Oscillator: A Theoretical Approach Boumali, Abdelmalek Garrah, Sarra Quantum Physics High Energy Physics - Theory We formulate the Dirac oscillator covariantly in the presence of external non-Abelian gauge fields. More precisely, the matter field is written as $Ψ_{αA}(x)$, where $α$ denotes the Dirac index and $A$ the isospin index, so that the Hamiltonian acts on the tensor-product space $\mathbb{C}^{4}\otimes\mathbb{C}^{2}$ in the fundamental representation. Starting from the gauge-covariant Dirac equation, we then implement the oscillator interaction through the standard non-minimal substitution and promote the construction to an $\mathrm{SU}(2)$ background. In this way, we derive the associated non-Abelian field-strength tensor and isolate the commutator contribution, which has no Abelian analogue. Consequently, the generalized Pauli interaction $σ^{μν}\mathcal{F}_{μν}$ produces matrix-valued spin--isospin couplings. At the same time, the Abelian sector reduces to the conventional Moshinsky--Szczepaniak Dirac oscillator, whose exactly solvable spectrum provides a natural benchmark for the extended theory. |
| title | Non-Abelian Extensions of the Dirac Oscillator: A Theoretical Approach |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.08978 |