Aharonov-Bohm-Like Scattering in the Generalized Uncertainty
Principle-corrected Quantum Mechanics
- URL: http://arxiv.org/abs/2101.08906v2
- Date: Thu, 8 Apr 2021 06:31:57 GMT
- Title: Aharonov-Bohm-Like Scattering in the Generalized Uncertainty
Principle-corrected Quantum Mechanics
- Authors: DaeKil Park
- Abstract summary: We compute the scattering cross section up to the first-order of the generalized uncertainty principle (GUP) parameter $beta$.
Unlike the usual Aharonv-Bohm scattering the cross section exhibits discontinuous behavior at every integer $alpha'$.
The symmetries, which the cross section has in the absence of GUP, are shown to be explicitly broken at the level of $cal O (beta)$.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: We discuss classical electrodynamics and the Aharonov-Bohm effect in the
presence of the minimal length. In the former we derive the classical equation
of motion and the corresponding Lagrangian. In the latter we adopt the
generalized uncertainty principle (GUP) and compute the scattering cross
section up to the first-order of the GUP parameter $\beta$. Even though the
minimal length exists, the cross section is invariant under the simultaneous
change $\phi \rightarrow -\phi$, $\alpha' \rightarrow -\alpha'$, where $\phi$
and $\alpha'$ are azimuthal angle and magnetic flux parameter. However, unlike
the usual Aharonv-Bohm scattering the cross section exhibits discontinuous
behavior at every integer $\alpha'$. The symmetries, which the cross section
has in the absence of GUP, are shown to be explicitly broken at the level of
${\cal O} (\beta)$.
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