The gauge-invariant angular momentum (or "kinetic angular momentum") is given by K = r × × ( p − − q A c ) , which has the commutation relations [ K i , K j ] = i ℏ ℏ ϵ ϵ i j k ( K k + q ℏ ℏ c x k ( x ⋅ ⋅ B ) ) where B = ∇ ∇ × × A is the magnetic field. The inequivalence of these two formulations shows up in the Zeeman effect and the Aharonov–Bohm effect.