Aharonov–Bohm effect

A quantum phenomenon in which electromagnetic potentials alter charged-particle interference even along paths where the electromagnetic field is zero.

Magnetic vector potential: A vector field whose curl gives the magnetic field and that enters the dynamics of charged particles. Its circulation around the solenoid sets the relative phase between paths.
Solenoid: A coil of wire that produces a magnetic field concentrated within its interior. The classic arrangement confines the magnetic field while particle paths pass outside.
Yakir Aharonov: An Israeli theoretical physicist known for foundational work in quantum mechanics. He co-proposed the effect showing potentials can influence quantum interference.
Classical electromagnetism: The classical theory describing electric and magnetic fields and their sources. Classical forces vanish along the idealized paths, unlike the quantum phase shift.
Gauge theory: A framework in which physical descriptions have local redundancies represented by gauge symmetries. The effect makes gauge potentials and their loop structure central to quantum observables.
Aharonov–Bohm phase: The quantum phase difference acquired by charged-particle paths enclosing magnetic flux. This phase shift directly produces the interference displacement.
Two-slit experiment: An experiment in which waves passing through two openings form an interference pattern. The two paths provide a direct setting for comparing phases around enclosed flux.
David Bohm: A theoretical physicist who developed an interpretation of quantum mechanics and contributed to quantum theory. He co-authored the 1959 paper introducing the effect.
Bohmian mechanics: An interpretation of quantum mechanics in which particles have definite positions guided by a wave function. Its account of the effect emphasizes the wave function's phase and guiding dynamics.
Aharonov–Casher effect: A quantum phase shift experienced by a magnetic dipole moving around an electric charge. It extends the effect's logic to particles with magnetic moments and electric sources.

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