Low-energy Compton scattering and poilarizabilities of hadrons

The amplitude of the interaction of the electromagnetic field with structural microparticles was defined on the basis of the gauge invariance approaches and the solutions of the electodynamics' equations using covariant method of the Green function. This amplitude is presented in terms of the electric and magnetic polarizations of compound system using no multipole expansion. In the framework of this approach the Lagrangian of the interaction of electromagnetic field with compound system and the Compton scattering amplitude were obtained taking into account electric and magnetic polarizabilities of the spin-$1/2$ particles.