As a result, even slow electrons in solids experience strong spin–orbit coupling. This means that the Hamiltonian of an electron in a crystal includes a coupling between the electron crystal momentum k = p / ℏ ℏ and the electron spin. The coupling to the external electric field can be found by substituting the momentum in the kinetic energy as k → → k − − ( e / ℏ ℏ c ) A , where A is the magnetic vector potential, as it is required by the gauge invariance of electromagnetism. The substitution is known as Peierls substitution. Thus, the electric field E = − − 1 c ∂ ∂ A / ∂ ∂ t becomes coupled to the electron spin and its manipulation may produce transitions between spin values.