An equivalent expression for the Hamiltonian as function of the relativistic (kinetic) momentum, ⁠ P = γ γ m x ˙ ˙ ( t ) = p − − q A ⁠, is H ( t ) = x ˙ ˙ ( t ) ⋅ ⋅ P ( t ) + m c 2 γ γ + q φ φ ( x ( t ) , t ) = γ γ m c 2 + q φ φ ( x ( t ) , t ) = E + V