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Path-integral approach to the tight-binding polaron is extended to multipleoptical phonon modes of arbitrary dispersion and polarization. The non-linearlattice effects are neglected. Only one electron band is considered. Theelectron-phonon interaction is of the density-displacement type, but can be ofarbitrary spatial range and shape. Feynman's analytical integration of iontrajectories is performed by transforming the electron-ion forces to the basisin which the phonon dynamical matrix is diagonal. The resulting polaron actionis derived for the periodic and shifted boundary conditions in imaginary time.The former can be used for calculating polaron thermodynamics while the latterfor the polaron mass and spectrum. The developed formalism is the analyticalbasis for numerical analysis of such models by path-integral Monte Carlomethods.Comment: 9 page

Polaron action for multimode dispersive phonon systems