Phi4 equations of motion. II. The zero-, one-, and two-dimensional solutions

This is the second paper of the series concerning the solution of the system of Phi4 equations of motion for the Schwinger functions by a fixed-point method. These works constitute a part of a general program towards the construction of a Phi44 Wightman quantum field theory (QFT). In the previous paper [J. Math. Phys. 29, 2092 (1988)] (Paper I), a general outline of the program has been presented. Moreover, the ''nice'' properties of signs, splitting, and norms revealed ''experimentally'' by the Phi iteration have been analyzed. We have shown how this iterative procedure converges to the solution (if the coupling constant is fixed positive and smaller than a finite value) thanks to the conservation of these properties, which constitute in fact a complete system of self-consistent conditions. Taking into account this information, in the present paper, the answer to the zero-, one-, and two-dimensional problems is given. To be precise, the fixed-point method is constructed by formulating the properties of signs and splitting of the Phi iteration in terms of particular subsets Phi0/sub Λ/ is contained inB-script0 (zero dimensions) and Phi/sub Λ/is contained inB-script (one and two dimensions) of the appropriated Banach spaces B-script0 and B-script, defined exactly with the norms provided by the Phi iteration