Abstract
A nonperturbative renormalization procedure is developed which is based on RG invariants, preserves the form of the action, and accounts systematically for the occurring parameter singularities. For the case of gauge fields a strictly gauge invariant description is worked out too. A basic set of RG invariant functions and the corresponding set of functions in the regularized theory are identified. The appropriate form of the lattice regularization is specified. For the sequence of regularized theories, which in the limit give the renormalized one, the parameter dependence is determined by a system of equivalence relations. Precise definitions of RG transformations and of a description dependence are given. The necessary properties of the basic lattice functions are investigated in detail. The emerging structure contains functions responsible for physical properties and ones describing parameter features and being absorbed into characteristic constants by the renormalization procedure. The solutions are shown to be consistent with respect to general RG transformations. The developed procedure is discussed and compared with different approaches.
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