Abstract
At the present stage of development of Lagrangian quantum field theory, information about model theories is available from several sources with quite different levels of mathematical completeness. For example, there is constructive quantum field theory, the results of which are typically mathematical theorems; it undertakes to construct solutions of specific models and then to establish their main properties with complete mathematical rigor. A second example is the analysis of high-energy and low-energy behavior using the method of the renormalization group. This analysis assumes that the models studied have solutions and deduces properties of those solutions from further assumptions (e.g. differentiability in parameters and the equivalence of a redefinition of the normalization of Green’s functions to a multiplicative renormalization) about the functions controlling high energy behavior. There are other sources of information; a complete list will not be given here.
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