Nonperturbative generating functionals in quantum field theory

To come towards a workable formulation of quantum field theory, which does not rely on perturbation theory, the definition of the generating functional for Green's functions by a sequence of finite expressions appears advantageous. In this sense a functional integral formulation on a finite lattice in 3 + 1 dimensions independent of the particular Lorentz frame is given. No reference to a space of states is needed. The formalism is checked for the scalar field and the noncompact Abelian gauge field. After a suitable modification the case of the compact Abelian gauge field is considered. (author)