## Abstract

Here, in our approximation of polaron theory, we examine the importance of introducing the*T* product, which turn out to be a very convenient theoretical approach for the calculation of thermodynamical averages.

We focus attention on the investigation of the so-called linear polaron Hamiltonian and present in detail the calculation of the correlation function, spectral function, and Green function for such a linear system.

It is shown that the linear polaron Hamiltonian provides an exactly solvable model of our system, and the result obtained with this approach holds true for an arbitrary coupling constant which describes the strength of interaction between the electron and the lattice vibrations. Then, with the help of a variational technique, we show the possibility of reducing the real polaron Hamiltonian to a socalled trial or approximate linear model Hamiltonian.

We also consider the exact calculation of free energy with a special technique that reduces calculations with the help of the T product, which, in our opinion, works much better and is easier than other analogous considerations, for example, the path-integral or Feynman-integral method.^{(1,2)}

Here we furthermore recall our own work,^{(4)} where it was shown that the results of Refs. 7 and 8 concerning the impedance calculation in the polaron model may be obtained directly without the use of the path-integral method.

The study of the polaron system's thermodynamics is carried out by us in the framework of the functional method. A calculation of the free energy and the momentum distribution function is proposed.

Note also that the polaron systems with strong coupling^{(9)} proved to be useful in different quantum field models in connection with the construction of dynamical models of composite particles. A rigorous solution of the special strong-coupling polaron problem, describing the interaction of a nonrelativistic particle with a quantum field, was given by Bogolubov.^{(3)} The works of Tavkhelidze, Fedyanin, Khrustalev, and others^{(10–13)} are dedicated to the further development and generalization of the Bogolubov method.

Notice, too, that the electron-photon interaction effects play an important part in many problems of modern solid state theory (see, e.g., Refs. 7 and 14–19).

The present paper summarizes a set of lectures delivered as a special course in the physics department of Moscow State University.

### Keywords

Analogous Consideration Polaron Model Arbitrary Coupling Solid State Theory Nonrelativistic Particle## Preview

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