Operator Changing Between Two Vacua of the ϕ⁴ Quantum Field Theory

In this note, we normal order the Hamiltonian of \phi^4 model to regularize the vacuum energy, based on canonical quantization. We perturbatively calculate the correction of the vacuum state to the second order, meanwhile at the first time get an operator that can change between two vacua of the \phi^4 quantum field theory. We believe this operator is at the same time the \phi^4 kink operator in a certain limit. In the end we give a brief introduction to the application of the vacuum energy.