Method of time-ordered products in polaron theory

The method of time-ordered products is used to investigate the equilibrium thermodynamic properties of the Frölich model in polaron theory. The polaron free energy at finite temperatures is calculated on the basis of Bogolyubov's variational principle. The trial functional is chosen in the most general form corresponding to an arbitrary number of harmonic oscillators interacting with the electron. An upper bound for the polaron ground-state energy is obtained and studied in the case of weak coupling and low temperatures. It is shown that the accuracy of the bound increases with increasing number of oscillators.