On the Feynman polaron

Kazuo Yamazaki

Ryuzo Abe, Ken‐ichi Okamoto

An improvement of the Feynman action is discussed by introducing two additional parameters to Feynman's original polaron theory. Both upper bounds of the ground state energy and corrections to the polaron mass are obtained for some values of the coupling constant. However, corrections are so small that Feynman's trial action is proved to be a very good description of the polaron state.

John T. Marshall, M. S. Chawla

In the expansion of the ground-state energy of a polaron in a weak magnetic field, the zeroth-order term is the polaron self-energy, while the first-order term is inversely proportional to the polaron effective mass. The effective mass so obtained is exactly equivalent to the freepolaron effective mass as defined by Fr\"ohlich. This equivalence principle is used to approximate the polaron effective mass by employing an approximate expression for the ground-state energy of a polaron in a weak magnetic field obtained by applying Feynman's path-integral variational method. The resultant polaron effective mass is found to be higher than Feynman's result by less than 1%.

Toshio Yokota

P. E. Kornilovitch

Feynman's formula for the effective mass of the Froehlich polaron is rederived from the formalism of projected partition functions. The mass is calculated as inverse of the diffusion coefficient of the polaron trajectory in imaginary time. It is shown that correlation between the electron and phonon boundary conditions in imaginary time is necessary for consistent derivation of the Feynman result.

Janusz Adamowski, B. Gerlach, Hajo Leschke