Feynman Path-Integral Calculation of the Polaron Effective Mass

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%.