Renormalization group and functional selfsimilarity in different branches of physics

A general formulation of “different” renormalization groups is given for different branches of physics-quantum field theory, the theory of kinetic phenomena, turbulence theory, polymer physics, the theory of radiative transfer. The unified formulation uses the language of group transformations and functional equations. The transformations and equations are based on a simple property, functional self-similarity, which is a generalization of ordinary self-similarity. The difference between the physical basis of the renormalization-group transformations in systems with infinitely large number of degrees of freedom and the functional self-similarity of simple physical systems is discussed.