Discussion of the principal methods of polaron theory

The concept of a polaron is introduced in a qualitative way and the most important theories are briefly discussed.
The results on the self-energy of the polaron derived by Lee, Low and Pines
are obtained here by generalizing the treatment of the interaction between a
particle with an infinite mass and a scalar field.
It is shown that in the Feynman theory of the polaron implicitly a coordinate defining approximately the "centre" of the polaron is incorporated.
The validity of the different methods is then discussed on the basis of
an exactly soluble polaron model.