Path-integral approach to single-particle excitation in Coulomb systems

The electron-plasmon Frohlich-type Hamiltonian, introduced by Lundquist, is formulated in terms of the Feynman and the Luttinger-Lu generalized path-integral approach. It is shown that the average propagator for the plasmaron, the dressing of the electron by plasmons, can be evaluated by using both approaches. The average propagator is then used to obtained the ground-state energy for the plasmaron. It is shown that the Luttinger-Lu approach gives higher ground-state energies than those obtained by the Feynman approach for intermediate values of the coupling constant and lower for the strong-coupling limit.