 The Lorenz gauge is a great simplification relative to Maxwell's field-strength approach to classical electrodynamics, and illustrates why it is useful to deal with excess degrees of freedom in the representation of the objects in a theory at the Lagrangian stage, before passing over to Hamiltonian mechanics via the Legendre transform.The Hamiltonian density is related to the Lie derivative of the Lagrangian density with respect to a unit timelike horizontal vector field on the gauge bundle.In a quantum mechanical context it is conventionally rescaled by a factor formula_1.