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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.30403 |
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| _version_ | 1866910270691999744 |
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| author | Boumali, Abdelmalek |
| author_facet | Boumali, Abdelmalek |
| contents | We investigate a planar Dirac oscillator coupled to a spatially uniform \(\utwo=\uone\times\su\) Yang--Mills background. The gauge configuration, adapted from the Dossa--Avossevou construction, contains an Abelian magnetic field \(B\), a non-Abelian spatial amplitude \(β\), and a non-Abelian scalar amplitude \(ρ\). Within the Pauli-reduced formulation, the non-Abelian field strength produces a constant operator on \(\mathbb{C}^{2}_{\mathrm{spin}}\otimes\mathbb{C}^{2}_{\mathrm{iso}}\). This operator contains a diagonal internal-Zeeman contribution proportional to \(σ^{3}T^{3}\) and an off-diagonal spin--isospin term proportional to \(σ^{1}T^{1}+σ^{2}T^{2}\). Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues \[ λ_{\mathrm{FM}}=\frac{g^{2}β^{2}}{4m},\qquad λ_{S}=-\frac{g^{2}β(β-2ρ)}{4m},\qquad λ_{T}=-\frac{g^{2}β(β+2ρ)}{4m}. \] Consequently, the aligned internal-Zeeman scale is quadratic in \(β\), whereas the singlet--triplet separation is linear in \(βρ\). The revised formulation makes the sign conventions explicit, verifies the main limiting cases, distinguishes the Pauli-reduced spectrum from a full first-order Dirac diagonalization, and clarifies the physical meaning of the numerical illustrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30403 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting Boumali, Abdelmalek High Energy Physics - Theory We investigate a planar Dirac oscillator coupled to a spatially uniform \(\utwo=\uone\times\su\) Yang--Mills background. The gauge configuration, adapted from the Dossa--Avossevou construction, contains an Abelian magnetic field \(B\), a non-Abelian spatial amplitude \(β\), and a non-Abelian scalar amplitude \(ρ\). Within the Pauli-reduced formulation, the non-Abelian field strength produces a constant operator on \(\mathbb{C}^{2}_{\mathrm{spin}}\otimes\mathbb{C}^{2}_{\mathrm{iso}}\). This operator contains a diagonal internal-Zeeman contribution proportional to \(σ^{3}T^{3}\) and an off-diagonal spin--isospin term proportional to \(σ^{1}T^{1}+σ^{2}T^{2}\). Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues \[ λ_{\mathrm{FM}}=\frac{g^{2}β^{2}}{4m},\qquad λ_{S}=-\frac{g^{2}β(β-2ρ)}{4m},\qquad λ_{T}=-\frac{g^{2}β(β+2ρ)}{4m}. \] Consequently, the aligned internal-Zeeman scale is quadratic in \(β\), whereas the singlet--triplet separation is linear in \(βρ\). The revised formulation makes the sign conventions explicit, verifies the main limiting cases, distinguishes the Pauli-reduced spectrum from a full first-order Dirac diagonalization, and clarifies the physical meaning of the numerical illustrations. |
| title | Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.30403 |