Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting
Abstract
We investigate a planar Dirac oscillator coupled to a spatially uniform utwo=uone×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 ℂ2spin⊗ℂ2iso. This operator contains a diagonal internal-Zeeman contribution proportional to σ3T3 and an off-diagonal spin--isospin term proportional to σ1T1+σ2T2. Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues λFM=g2β2/4m, λS=−(g2β(β−2ρ))/4m, λT=−(g2β(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.
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BibTeX
@misc{boumali2026nonabelian,
title = {{Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting}},
author = {Abdelmalek Boumali},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.30403},
eprint = {2605.30403},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30403},
note = {CC0},
}
RIS
TY - UNPB
TI - Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting
AU - Abdelmalek Boumali
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2605.30403
UR - https://arxiv.org/abs/2605.30403
AB - We investigate a planar Dirac oscillator coupled to a spatially uniform utwo=uone×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 ℂ^2_spin⊗ℂ^2_iso. This operator contains a diagonal internal-Zeeman contribution proportional to σ^3T^3 and an off-diagonal spin--isospin term proportional to σ^1T^1+σ^2T^2. Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues λ_FM=g^2β^2/4m, λ_S=−(g^2β(β−2ρ))/4m, λ_T=−(g^2β(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.
ER -