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Effective field theory of magnetic and resistive properties of manganiteswith account of strong Hund exchange coupling and electron-phonon interactionshas been evolved under the strong Hund coupling condition. In parallel withLang-Firsov unitary transformation of the zeroth Hamiltonian, we have realizedthe diagonalization of Hund's Hamiltonian neglecting the upper triplet. Thediagram techniques taking into account the quantum spin fluctuations of lowerquintet and hole state with spin S=3/2 was developed. The magnetic structure ofthe ground state and an influence of electron-phonon interaction have beenanalyzed using the first nonvanishing approximation of perturbation theory. Thecalculated temperature dependence of resistivity agrees well with experimentaldata including these obtained in applied magnetic field.Comment: 44 pages, 14 figure

Diagrammatic method for the theory of magnetic and resistive properties of manganites