 Integrating it by parts over a spacelike cross section recovers the form of the integrand familiar from canonical quantization.Because the definition of the Hamiltonian involves a unit time vector field on the base space, a horizontal lift to the bundle space, and a spacelike surface "normal" (in the Minkowski metric) to the unit time vector field at each point on the base manifold, it is dependent both on the connection and the choice of Lorentz frame, and is far from being globally defined.But it is an essential ingredient in the perturbative framework of quantum field theory, into which the quantized Hamiltonian enters via the Dyson series.