How can you tell if the Klein-Gordan Hamiltonian, [tex]H=\int d^3 x \frac{1}{2}(\partial_t \phi \partial_t \phi+\nabla^2\phi+m^2\phi^2) [/tex] is time-independent? Don't you have to plug in the expression for the field to show this? But isn't the only way you know how the field evolves with time is through [tex]\partial_t \phi=i[H,\phi] [/tex], and in order to evaluate this you have to assume the Hamiltonian is independent of time to use the equal-time commutation relations?