= Heisenberg equation of motion
{c}
{title2=$\dot O_H=i[H_H,O_H]+U^\dagger\partial_tO_SU$}
= Heisenberg equations of motion
{c}
{synonym}
For an operator $O_H=U^\dagger O_SU$ in the <Heisenberg picture>, differentiating the evolution operators gives $dO_H/dt=i[H_H,O_H]+U^\dagger(\partial O_S/\partial t)U$ in units $\hbar=1$. With no explicit operator time dependence, the second term vanishes. Applying this <commutator> identity to the <canonical momentum> and <real scalar field> gives their operator field equations.
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