Convergence of lattice approximations and infinite volume limit in the (λφ4−σφ2−μφ)3 field theory

Abstract

By unified method we prove the convergence of the lattice approximation of the (λφ4−σφ2−ψφ)3 field model with periodic, Dirichlet and Neumann boundary conditions in a finite box. This then allows us to take the inifinite volume limit of the Dirichlet states by the Nelson’s monotonicity argument. The model under consideration satisfies all the Wightman axioms except possibly the uniqueness of vacuum for μ=0 and the mass gap.