A retarded action functional for the Dirac polaron

The ground-state characteristics of the one-dimensional (Dirac) polaron are considered as an example of a system with a retarded interaction functional. Using a path-integral approach, we estimate both the ground-state energy and the effective mass of the polaron within and beyond the most general Gaussian approximation. The leading-order Gaussian contribution to the self-energy slightly improves the Feynman estimate and belongs to the lowest upper bounds available. The next-to-leading non-Gaussian corrections do not significantly perturb the results obtained. For comparison, a lower bound to the ground-state energy is calculated using the Lieb–Yamazaki method.