We consider a strong-coupling approach to λφ4-meson theory as formulated in a lattice space which is of simple cubic type having lattice constanta and total volumeV. Self-adjointness and regularity of the Hamiltonian are established. The strong-coupling perturbation series are examined for the cases with and without mass renormalization. The series for ground state and one-particle state as well as for their energies are shown to converge when the coupling constant is sufficiently large, say λ>λ c (sufficient condition). The bounds λ c we have found increase with the total volumeV and/or the cut-off momentuma −1. Some other features of the strong-coupling perturbation theory are also discussed.
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Ezawa, H. Remarks on the quantum field theory in lattice space. II. Commun.Math. Phys. 9, 38–52 (1968). https://doi.org/10.1007/BF01654030
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