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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

The inadmissibility of non-Stokesian vector potentials in quantum mechanics. Comments on a paper asserting the nonexistence of the Aharonov-Bohm effect

U. Klein

Published May 1, 1979• 18 citations
Publisher
DOI
10.1007/bf02789531

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Comment on "Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases"

Shan Gao

Marletto and Vedral [Phys. Rev. Lett. 125, 040401 (2020)] propose that the Aharonov-Bohm (AB) phase is locally mediated by entanglement between a charged particle and the quantized electromagnetic field, asserting gauge independence for non-closed paths. In this Comment, we critically analyze their model and demonstrate that the AB phase arises from the interaction with the vector potential \(\mathbf{A}\), not from entanglement, which is a byproduct of the quantum electrodynamics (QED) framework. We show that their field-based energy formulation, intended to reflect local electromagnetic interactions, is mathematically flawed due to an incorrect prefactor and yields \( +q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} \) in the Coulomb gauge, conflicting with QED's \( -q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} \). This equivalence to \( q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} \) holds only approximately in the Coulomb gauge under static conditions, failing for time-dependent fields and other gauges, undermining their claim of a gauge-independent local mechanism. Furthermore, we confirm that the AB phase is gauge-dependent for non-closed paths, contradicting their assertion. Our analysis reaffirms the conventional explanation in the semi-classical picture, where the AB phase is driven by the vector potential \(\mathbf{A}\), with entanglement playing no causal role in its generation.

quant-pharXiv:2601.17665•Physical Review Letters•Jan 27, 2026•3 citations

Nonexistence of the Aharonov-Bohm effect

P. Bocchieri, A. Loinger

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields•Oct 1, 1978•124 citations
Marletto and Vedral [Phys. Rev. Lett. 125, 040401 (2020)] propose that the Aharonov-Bohm (AB) phase is locally mediated by entanglement between a charged particle and the quantized electromagnetic field, asserting gauge independence for non-closed paths. In this Comment, we critically analyze their model and demonstrate that the AB phase arises from the interaction with the vector potential A\mathbf{A}A, not from entanglement, which is a byproduct of the quantum electrodynamics (QED) framework. We show that their field-based energy formulation, intended to reflect local electromagnetic interactions, is mathematically flawed due to an incorrect prefactor and yields +qv⋅As +q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} +qv⋅As​ in the Coulomb gauge, conflicting with QED's −qv⋅As -q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} −qv⋅As​. This equivalence to qv⋅As q \mathbf{v} \cdot \mathbf{A}_{\mathbf{s}} qv⋅As​ holds only approximately in the Coulomb gauge under static conditions, failing for time-dependent fields and other gauges, undermining their claim of a gauge-independent local mechanism. Furthermore, we confirm that the AB phase is gauge-dependent for non-closed paths, contradicting their assertion. Our analysis reaffirms the conventional explanation in the semi-classical picture, where the AB phase is driven by the vector potential A\mathbf{A}A, with entanglement playing no causal role in its generation.