RELATIONSHIP BETWEEN THE 2-DIMENSIONAL PSIBAR-PSI-PSIBAR-PSI MODEL AND YUKAWA-TYPE MODELS

We show to all orders in mean-field perturbation theory that a two-dimensional scalar four-fermion interaction (ψ̄ψ)2 has renormalized Green's functions which are structurally identical to an infinite class of theories having fundamental Yukawa-type couplings with a scalar field σ and additional scalar self-interactions of the form F(σ). For a particular choice of renormalized parameters of the Yukawa-type theories which occurs as Zσ3→0 the renormalized Green's functions are numerically equal to those of the four-fermion theory. © 1979 The American Physical Society.