 This Lagrangian, combined with Euler–Lagrange equation, produces the Lorentz force law

and is called minimal coupling.Note that the values of scalar potential and vector potential would change during a gauge transformation, and the Lagrangian itself will pick up extra terms as well; But the extra terms in Lagrangian add up to a total time derivative of a scalar function, and therefore still produce the same Euler-Lagrange equation.The canonical momenta are given by