Proving the time-evolution of momentum operator

Question

In QFT the evolution of momentum and field operators is given by $∂_0φ=i[H,φ]$ and $∂_0\pi=i[H,\pi]$.

Is it possible to derive these equations from the basic operator commutation relations or are they postulated?

Note: this is a follow-up to Canonical quantization of quantum field

Answer 1

The basic canonical commutation relations are equal time relations, which carry no information about evolution. In the operator formalism, the Heisenberg equations of motion are postulated as evolution equations.