Effective theories and bootstrap equations

In this paper we consider the general properties of effective field theories. We note that the freedom to fix the renormalization conditions in the effective field theory is not as large as it seems. The consideration of minimal set of correctness requirements of the perturbative scheme based on the Dyson's formula for $S$-matrix leads to severe restriction on the essential parameters of the theory and hence on the possible set of renormalization conditions.
In the first part of this paper we make a short review of the structure of the localizable effective field theories. We discuss the necessary conditions that ensure the correctness of the first step of the iterative scheme of calculation of $S$-matrix – the construction of the tree-level amplitudes. In the second part we bring the examples that demonstrate the main stages of acquisition and analysis of the system of bootstrap equations.