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 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 Gauge-Underdetermination and Shades of Locality in the Aharonov–Bohm Effect

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Ruward A. Mulder
Keyword(s):  
Magnetic Fields ◽  
Equivalence Class ◽  
Explanatory Power ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Gauge Equivalence ◽  
Electric And Magnetic Fields ◽  
Lorenz Gauge ◽  
Bohm Effect ◽  
Aharonov Bohm

AbstractI address the view that the classical electromagnetic potentials are shown by the Aharonov–Bohm effect to be physically real (which I dub: ‘the potentials view’). I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into ‘gauge-underdetermination’: different gauge choices represent different physical states of affairs and hence different theories. This fact is usually not acknowledged in the literature (or in classrooms), neither by proponents nor by opponents of the potentials view. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields (which I call the Wide Equivalence Class) is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. On the one hand, this narrower equivalence class gives a local explanation of the AB effect in the sense that the phase is incrementally picked up along the path of the electron. On the other hand, locality is not satisfied in the sense of signal locality, viz. the finite speed of propagation exhibited by electric and magnetic fields. It is therefore intellectually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. will prefer some elements of such an equivalence class over others. I consider various formulations of locality, such as Bell locality, local interaction Hamiltonians, and signal locality. I show that Bell locality can only be evaluated if one fixes the gauge freedom completely. Yet, an explanation in terms of signal locality can be accommodated by the Lorenz gauge: the potentials propagate in waves at finite speed. I therefore suggest the Lorenz gauge potentials theory—an even narrower gauge equivalence relation—as the ontology of electrodynamics.

INVARIANT SOLUTION OF THE DIRAC EQUATION IN THE CROSSED ELECTRIC AND MAGNETIC FIELDS $ (H \mathclose{>} E) $

2019 ◽  
Vol 53 (2 (249)) ◽  
pp. 138-141
Author(s):  
R.G. Petrosyan ◽  
M.A. Davtyan
Keyword(s):  
Dirac Equation ◽  
Magnetic Fields ◽  
Harmonic Oscillator ◽  
Invariant Solution ◽  
Charged Particles ◽  
Invariant Solutions ◽  
Quantum Harmonic Oscillator ◽  
Electric And Magnetic Fields

In the article exact analytical and invariant solutions for both spinless and half-spin relativistic charged particles in crossed constant electric and magnetic fields, when $ H \mathclose{>} E $ have been found. It is shown that in both cases the problem reduces to that of quantum harmonic oscillator.

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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