Spectral Reduction Selects the Observable Imprint of Dirac Quantum Geometry
Abstract
Spectral constraints can alter the observable manifestation of quantum geometry without changing the local eigenspace. Relativistic electron vortices provide a sharp example: the spin orbit interaction redistributes spin and orbital angular momentum, yet its magnetic contribution differs between localized three-dimensional wave packets and stationary monochromatic beams. We resolve this discrepancy by showing that fixing the energy replaces ambient momentum derivatives in position-weighted current moments by shell-tangent derivatives and derive a Hermitian selection rule for first-order observables in momentum-dependent internal subspaces. Its extension-independent form applies beyond Dirac systems, including a broad class of antisymmetric first moments of scalar-charge velocity currents. For the free positive-energy Dirac doublet, the magnetic correction is an exact non-Abelian Berry-curvature contraction with a pointwise saturable quantum-metric bound. Changing the relative phase between the two σz spinor components switches this correction from zero in a conserved transverse-helicity sector to a finite value in a radial coherent superposition. At fixed finite Lorentz factor, the radial response scales as O(θ/γ), compared with O(θ2) for longitudinal polarization. Spectral reduction and internal coherence thus provide distinct controls of the observable imprint of quantum geometry.
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BibTeX
@misc{guo2026spectral,
title = {{Spectral Reduction Selects the Observable Imprint of Dirac Quantum Geometry}},
author = {Zhongze Guo and Bei Xu and Qiang Gu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38379},
eprint = {2610.38379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38379},
}
RIS
TY - UNPB
TI - Spectral Reduction Selects the Observable Imprint of Dirac Quantum Geometry
AU - Zhongze Guo
AU - Bei Xu
AU - Qiang Gu
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38379
UR - https://arxiv.org/abs/2610.38379
AB - Spectral constraints can alter the observable manifestation of quantum geometry without changing the local eigenspace. Relativistic electron vortices provide a sharp example: the spin orbit interaction redistributes spin and orbital angular momentum, yet its magnetic contribution differs between localized three-dimensional wave packets and stationary monochromatic beams. We resolve this discrepancy by showing that fixing the energy replaces ambient momentum derivatives in position-weighted current moments by shell-tangent derivatives and derive a Hermitian selection rule for first-order observables in momentum-dependent internal subspaces. Its extension-independent form applies beyond Dirac systems, including a broad class of antisymmetric first moments of scalar-charge velocity currents. For the free positive-energy Dirac doublet, the magnetic correction is an exact non-Abelian Berry-curvature contraction with a pointwise saturable quantum-metric bound. Changing the relative phase between the two σ_z spinor components switches this correction from zero in a conserved transverse-helicity sector to a finite value in a radial coherent superposition. At fixed finite Lorentz factor, the radial response scales as O(θ/γ), compared with O(θ^2) for longitudinal polarization. Spectral reduction and internal coherence thus provide distinct controls of the observable imprint of quantum geometry.
ER -