Maxwell Duality, Lorentz Invariance, and Topological Phase

Abstract

We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena. We also elucidate Lorentz transformations that allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose two experimental schemes for measuring the He-McKellar-Wilkens phase.

10 pages, 2 figures

Cited by in corpus (45)

• Atom Interferometers
• On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds
• The HMW effect in Noncommutative Quantum Mechanics
• He-McKellar-Wilkens topological phase in atom interferometry
• Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law
• He-McKellar-Wilkens effect and Scalar Aharonov-Bohm effect for a neutral particle based on the Lorentz symmetry violation
• Quantum Dynamics of Magnetic and Electric Dipoles and Berry's Phase
• Quantum Holonomies based on the Lorentz-violating tensor background
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Solid State Analog for He-McKellar-Wilkens Quantum Phase
• On an atom with a magnetic quadrupole moment subject to harmonic and linear confining potentials
• Quantum gates with topological phases
• The Topological AC and HMW Effects, and the Dual Current in 2+1 Dimensions
• Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension
• Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states
• Charged particle interferometry in Plebański--Demiański black hole space--times
• Flux Quantization Due to Monopole and Dipole Currents
• Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics
• Energy level shift of quantum systems via the electric Aharonov-Bohm effect
• Photon mass and quantum effects of the Aharonov-Bohm type
• Local/Non-Local Complementarity in Topological Effects
• Test of the He-McKellar-Wilkens topological phase by atom interferometry. Part I: theoretical discussion
• Topology, nonlocality and duality in classical electrodynamics
• Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials
• The He-McKellar-Wilkens effect for spin one particles in non-commutative quantum mechanics
• Relativistic dipole interaction and the topological nature for induced HMW and AC phases
• Testing Bell-CHSH Inequalities Using topological Aharonov-Casher and He-McKellar-Wilkens Phases
• Revisiting the missing He-McKellar-Wilkens geometric quantum phase
• Entanglement of topological phase factors
• Hybird of Quantum Phases for Induced Dipole Moments
• Flux-free conductance modulation in a helical Aharonov-Bohm interferometer
• Correspondences and Quantum Description of Aharonov-Bohm and Aharonov-Casher Effects
• Magnetic Properties of Scalar Particles --The Scalar Aharonov-Casher Effect and Supersymmetry
• Time-dependent Aharonov-Bohm type topological effects on dipoles
• On the geometric phases in entangled states
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• The quantum phase of a dyon
• Momentum of electromagnetic fields, speed of light in moving media, and the photon mass
• Precession and interference in the Aharonov-Casher and scalar Aharonov-Bohm effect
• Electromagnetic response in dipole superfluids: vortex lattices and singular domain walls
• Geometric phase of a moving dipole under a magnetic field at a distance
• Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles
• Dyons with phase ${\delta }_{\theta }=n\theta$
• Realization of cyons and anyons by atoms
• Induced electric dipole moment coupling in Dirac equation