Galilean covariance almost fixes the quantum probability current
In plain wordsConservation alone does not fix how quantum probability flows; for any current built from a one-body operator, behaving correctly under a change to a moving frame leaves the standard current plus a density term, which rotation symmetry in three or more dimensions, or one translation relation, removes.
The result
As the paper states it, in briefThe continuity equation fixes only the divergence of the quantum probability current. Imposing Galilean boost covariance pointwise, for any one-body current, local or nonlocal, pure, mixed or many-body, leaves exactly the Schrödinger current plus a linear functional of the density; rotational covariance with conservation removes that term in three or more dimensions, and conservation with the momentum–translation relation removes it in every dimension. The same framework sorts the known alternatives, among them Nelson’s, Doebner–Goldin, chiral and Deotto–Ghirardi currents.
Questionson the index
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Novelty and credit
- Novelty
- Extends named prior work: Holland’s results on the uniqueness of conserved currents and Deotto and Ghirardi’s alternative guidance laws, credited in the paper.
Versionsone, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| — | 10.5281/zenodo.23815695 |
Paper, code and links
- Paper
On Zenodo: doi:10.5281/zenodo.23815695. No copy is hosted here.
Corrections
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Cite
@misc{mghirbi2026probabilitycurrent,
author = {Mghirbi, Nidhal},
title = {Galilean covariance almost fixes the quantum probability current},
year = {2026},
doi = {10.5281/zenodo.23815695},
url = {https://doi.org/10.5281/zenodo.23815695}
}