The Constrained State of Minimum Energy and the Effective Equation of Motion

We define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the quantum field theory. As an example, we consider the scalar field with λ/4!Φ4 interaction. To the third order of perturbation, we obtain the equation of motion of the dynamic expectation value of the scalar field in the defined state.