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?(adsbygoogle = window.adsbygoogle || []).push({});

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# Klein-gordan Hamiltonian time-independent?

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