Parallel Transport & Holonomy on a Sphere — Fiber Bundle Gauge Theory

Latitude θ: 45° Loop size φ: 360° Speed: 1x Reset Pause

Holonomy angle: 0.00° | Solid angle Ω: 0.00 sr | Berry phase: 0.00 rad

A vector parallel-transported around a closed loop on a sphere returns rotated by a holonomy angle equal to the solid angle Ω enclosed. This geometric phase (Berry phase) is purely topological — independent of the path speed. In gauge theory, this is the holonomy of a connection on a fiber bundle; in quantum mechanics, γ = -Ω/2 for spin-1/2 systems.