scholarly journals Generalized Strichartz estimates for wave and Dirac equations in Aharonov–Bohm magnetic fields

2022 ◽  
Vol 19 (1) ◽  
pp. 71-90
Author(s):  
Federico Cacciafesta ◽  
Zhiqing Yin ◽  
Junyong Zhang
Keyword(s):  
Magnetic Fields ◽  
Strichartz Estimates ◽  
Dirac Equations ◽  
Aharonov Bohm

scholarly journals The Quaternionic Commutator Bracket and Its Implications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 513 ◽  
Author(s):  
Arbab Arbab ◽  
Mudhahir Al Ajmi
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Interaction Energy ◽  
Internal Structure ◽  
Magnetic Moments ◽  
Electric And Magnetic Fields ◽  
Aharonov Bohm

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. ψ ˜ = ( i c ψ 0 , ψ → ) , represents a state of a particle with orbital angular momentum, L = 3 ℏ , resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector ψ → , points in an opposite direction of L → . When a charged particle is placed in an electromagnetic field, the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov–Bohm and Aharonov–Casher effects.

scholarly journals A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1191 ◽  
Author(s):  
Joan Bernabeu ◽  
Jose Navarro-Salas
Keyword(s):  
Electromagnetic Field ◽  
Magnetic Fields ◽  
Harmonic Oscillator ◽  
Local Action ◽  
Action Functional ◽  
Duality Symmetry ◽  
Electric And Magnetic Fields ◽  
Non Local ◽  
Bohm Effect ◽  
Aharonov Bohm

A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov–Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner.

scholarly journals Symmetry Results in Two-Dimensional Inequalities for Aharonov–Bohm Magnetic Fields

2019 ◽  
Vol 375 (3) ◽  
pp. 2071-2087 ◽  
Author(s):  
Denis Bonheure ◽  
Jean Dolbeault ◽  
Maria J. Esteban ◽  
Ari Laptev ◽  
Michael Loss
Keyword(s):  
Magnetic Fields ◽  
Two Dimensional ◽  
Aharonov Bohm

Precise period doubling of the Aharonov-Bohm effect in a quantum dot at high magnetic fields

1996 ◽  
Vol 53 (7) ◽  
pp. 3642-3645 ◽  
Author(s):  
J. P. Bird ◽  
K. Ishibashi ◽  
Y. Aoyagi ◽  
T. Sugano
Keyword(s):  
Magnetic Fields ◽  
Quantum Dot ◽  
Period Doubling ◽  
High Magnetic Fields ◽  
Bohm Effect ◽  
Aharonov Bohm
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