Operator ordering as an emergent geometric background in Dirac systems with spatially varying mass
Abstract
We investigate the spectral consequences of the uniquely determined Hermitian ordering of the Dirac Hamiltonian with spatially varying mass. In contrast to the nonrelativistic case, where continuous families of admissible prescriptions exist, the relativistic Dirac operator admits a single consistent ordering compatible with probability-current conservation. This requirement generates an additional logarithmic-gradient term proportional to the spatial variation of the mass profile. We show that this contribution modifies the effective kinetic operator and induces a universal deformation of the spectral quantization condition. In compact geometry, an explicit analytic computation reveals a mode-dependent second-order spectral shift that becomes strongly enhanced near the mass-inversion threshold. These results demonstrate that the consistent relativistic ordering of the Dirac operator leads to observable modifications of discrete spectra in spatially inhomogeneous scalar backgrounds.
Versions
Related
- Geometric origin of oxygen ordering and the solubility limit in niobium
- Geometric Ginzburg-Landau theory of charge ordering and commensurability
- Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation
- Using Geometric Deep Learning for the Detection of the Diffuse Supernova Neutrino Background in Water-Cherenkov Detectors
- Emergent Quantum Geometric Phases in Holey Graphene
BibTeX
@misc{almeida2026operator,
title = {{Operator ordering as an emergent geometric background in Dirac systems with spatially varying mass}},
author = {C. A. S. Almeida},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.14148},
eprint = {2605.14148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14148},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Operator ordering as an emergent geometric background in Dirac systems with spatially varying mass
AU - C. A. S. Almeida
PY - 2026
DA - 2026/05/13
PB - arXiv
DO - 10.48550/arxiv.2605.14148
UR - https://arxiv.org/abs/2605.14148
AB - We investigate the spectral consequences of the uniquely determined Hermitian ordering of the Dirac Hamiltonian with spatially varying mass. In contrast to the nonrelativistic case, where continuous families of admissible prescriptions exist, the relativistic Dirac operator admits a single consistent ordering compatible with probability-current conservation. This requirement generates an additional logarithmic-gradient term proportional to the spatial variation of the mass profile. We show that this contribution modifies the effective kinetic operator and induces a universal deformation of the spectral quantization condition. In compact geometry, an explicit analytic computation reveals a mode-dependent second-order spectral shift that becomes strongly enhanced near the mass-inversion threshold. These results demonstrate that the consistent relativistic ordering of the Dirac operator leads to observable modifications of discrete spectra in spatially inhomogeneous scalar backgrounds.
ER -