Uniform bounds of the Schwinger functions in boson field models

Abstract

We study the lattice and space cutoff boson field models with periodic boundary condition in d‐dimensional space–time (d‐N⁺). We prove that if the pressures of the interaction (and also the pressures of the interaction with linear external fields) under consideration are bounded uniformly in the cutoffs, the corresponding Schwinger functions are also bounded uniformly in the cutoffs. By applying the above result we prove the uniform bounds of the space cutoff Schwinger functions for the (λφ⁴−σφ²−μφ)₃ model and the lattice and space cutoff Schwinger functions for the exponential type interactions in d‐dimensional space–time.