Soluble covariant nonrenormalizable quantum field theory

The Green's-function generating functional for each model of a certain class of covariant nonrenormalizable quantum field theories is derived. The models involve an Abelian gauge vector field ${\phi }_{\mu }$ in a two-dimensional space-time, and are based on Lagrangian densities of the form $\mathfrak{L}\left[f_{\mu \nu }\mathrm{}\right(x\left)\right]=-\frac{1}{4}{f}_{\mu \nu }\mathrm{}\left(x\right)\mathrm{}{f}^{\mu \nu }\mathrm{}\left(x\right)+\lambda {\mathfrak{L}}^{\prime }[-\frac{1}{4}{f}_{\mu \nu }\mathrm{}(x\left)\mathrm{}{f}^{\mu \nu }\mathrm{}\right(x\left)\right]$, where $f_{\mu \nu }\equiv {\partial }_{\mu }{\phi }_{\nu }|-\partial {\phi }_{\mu }$ and ${\mathfrak{L}}^{\prime }$ is nonlinear. Fundamental differences in an operator realization between the free theory and every interacting theory are noted for these models.