POLARON GROUND-STATE ENERGY IN D-DIMENSIONS

The polaron path integral introduced by Feynman is generalized to the case of an electron moving in d space dimensions. A scheme of systematic calculations of the obtained path integral is developed to estimate the ground-state energy of the polaron in the same way for different values of the electron-phonon coupling constant alpha. The leading-order term in this approach yields an upper bound to the polaron self-energy and improves Feynman's variational estimates for d = 2 and d = 3. A scaling relation between polaron self-energies for different space dimensions is obtained for this term. The next correction to this estimation is calculated by numerical integration for d = 2 and d = 3.