Verification of axioms for Euclidean and relativistic fields and Haag's theorem in a class of P(phi)2-models

Axioms for Euclidean (Bose) fields are proposed and shown to suffice for the reconstruction of relativistic quantum fields satisfying the Wightman axioms. Those axioms are verified for a class of P(phi)2 models. They seem to provide a suitable framework for (Bose) field theories in two and three space-time dimensions. It is shown that the P(phi)2-interacting field in the infinite volume limit is not a (generalized) free field or a wick polynomial of a (generalized) free field. If P1 and P2 are two interaction polynomials in the region of convergence of the Glimm-Jaffe-Spencer cluster expansion then the corresponding infinite volume field theories are different, unless P1(xi)=P2(+-xi+a)+b