The first order expansion of a ground state energy of the ϕ4 model with cutoffs

In this paper, we investigate the $\phi^4$ model with cutoffs. By introducing a spatial cutoff and a momentum cutoff, the total Hamiltonian is a self-adjoint operator on a boson Fock space. Under regularity conditions of the momentum cutoff, we obtain the first order expansion of a non-degenerate ground state energy of the total Hamiltonian.