Here A is the magnetic vector potential and ϕ the electric potential, both representing the electromagnetic field, and σ = (σ x, σ y, σ z) are the Pauli matrices. On squaring out the first term, a residual interaction with the magnetic field is found, along with the usual classical Hamiltonian of a charged particle interacting with an applied field: H = 1 2 m ( p − − e c A ) 2 + e ϕ ϕ − − e ℏ ℏ 2 m c σ σ ⋅ ⋅ B .