which is of order v ⁄ c - thus at typical energies and velocities, the bottom components of the Dirac spinor in the standard representation are much suppressed in comparison to the top components. Substituting this expression into the first equation gives after some rearrangement ( E − − m c 2 ) ψ ψ + = 1 2 m [ σ σ ⋅ ⋅ ( p − − e c A ) ] 2 ψ ψ + + e ϕ ϕ ψ ψ +