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Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions
Quantum Physics · Submitted 27 Jul 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level.
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The abstract, sentence by sentence
The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. The scattering problem for such two-body systems is extended to the relativistic case, and the scattering amplitude is obtained as a partial wave series. The electric charge and magnetic flux is ($-q$, $-\phi/Z$) for one particle and ($Zq$, $\phi$) for the other. When $(Zq^2/\hbar c)^2\ll 1$, and $q\phi/2\pi\hbar c$ takes on integer or half integer values, the partial wave series is summed up approximately to give a closed form. The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. | background 1.00 | 0.09 | 0.04 | hedged possibility 1.00 |
| s1 | The scattering problem for such two-body systems is extended to the relativistic case, and the scattering amplitude is obtained as a partial wave series. | contribution 0.96 | 0.90 | 0.15 | asserted 1.00 |
| s2 | The electric charge and magnetic flux is ($-q$, $-\phi/Z$) for one particle and ($Zq$, $\phi$) for the other. | method 0.66 | 0.35 | 0.03 | asserted 1.00 |
| s3 | When $(Zq^2/\hbar c)^2\ll 1$, and $q\phi/2\pi\hbar c$ takes on integer or half integer values, the partial wave series is summed up approximately to give a closed form. | result 0.54 | 0.89 | 0.16 | asserted 0.98 |
| s4 | The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level. | interpretation 0.82 | 0.86 | 0.40 | asserted 1.00 |
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Original abstract
The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. The scattering problem for such two-body systems is extended to the relativistic case, and the scattering amplitude is obtained as a partial wave series. The electric charge and magnetic flux is ($-q$, $-\phi/Z$) for one particle and ($Zq$, $\phi$) for the other. When $(Zq^2/\hbar c)^2\ll 1$, and $q\phi/2\pi\hbar c$ takes on integer or half integer values, the partial wave series is summed up approximately to give a closed form. The results exhibit some nonperturbative features and cannot be obtained from perturbative quantum electrodynamics at the tree level.
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It is shown that the principal results of a recent work by Khalilov are incorrect.
Comment on "Relativistic Aharonov-Bohm effect in the presence of planar Coulomb potentials" · 0.96
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