For the system of the quasiparticles interacting with arbitrary number of phonon modes at T=0 K on the basis of the Feinman diagram technique the exact representation of the Green function in the form of the infinite branching integral fraction was obtained. It is shown that thus the developed method of the calculation of the Green functions monotypically takes into account virtual many-phonon processes, it gives an opportunity to obtain the spectrum of the system at the arbitrary binding values and in any region of energies and quasiimpulses quickly and effectively. It is established that in the system of dispersionless quasiparticles interacting with many-mode phonons the excited states are convergent infinite series of energy levels.Comments: Figs. 4, Refs. 13, Tabs. 0.
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