AHARONOV-BOHM EFFECT

Interference from vector potential — topology without local force

MAGNETIC FLUX

Φ₀ = h/e = flux quantum
Phase shift: Δγ = 2πΦ/Φ₀

OBSERVABLES

AB phase Δγ:0.000
Fringe shift:0.000 Δy
|B| outside:0 (always)
Vector potential A:nonzero

ELECTRON PATHS

Path 1 (above):γ₁
Path 2 (below):γ₂
Phase diff:0.00 rad
Even with B=0 outside solenoid,
the vector potential A≠0 causes
a measurable phase shift Δγ=e/ℏ∮A·dl
= eΦ/ℏ = 2πΦ/Φ₀