Holonomy Angle
0.00°
= Solid Angle Ω enclosed
0.00 sr
= 2π·sin(λ)·Δφ/2π
Holonomy = Solid Angle:
Δθ = ∮ A·dl = Ω(loop)
Berry Phase (quantum):
γ = i∮⟨n|∇_R|n⟩·dR
Foucault pendulum:
Δφ = 2π sin(λ)
(latitude λ, full day rotation)
Δθ = ∮ A·dl = Ω(loop)
Berry Phase (quantum):
γ = i∮⟨n|∇_R|n⟩·dR
Foucault pendulum:
Δφ = 2π sin(λ)
(latitude λ, full day rotation)
A vector parallel-transported around a closed loop on a curved surface returns rotated by an angle equal to the solid angle enclosed — holonomy of the tangent bundle.