Bootstrap Equations in Effective Theories

In this paper, we consider general properties of effective field theories. We note that the freedom of fixing renormalization conditions in the effective field theory is not as large as it seems. Consideration of the minimal set of correctness requirements of the perturbative scheme based on the Dyson's formula for the S-matrix leads to severe restrictions on essential parameters of the theory and hence on the possible set of renormalization conditions. In the first part of this paper, we give a short review of the structure of localizable effective field theories. We discuss necessary conditions which ensure the correctness of the first step of the iterative scheme of calculation of the S-matrix, i.e., the construction of tree-level amplitudes. In the second part, we discuss examples which demonstrate the main stages of acquisition and analysis of the system of bootstrap equations. Bibliography: 17 titles.