Strong coupling polaron theory and translational invariance

Abstract

We develop a systematic, manifestly translation invariant, strong coupling theory for nonrelativistic Hamiltonians of the polaron type. As in earlier strong coupling theories, the position of the polarization well is a collective coordinate. The field is expanded in a set of basis functions centered about the well with three amplitudes deleted. A particle coordinate relative to the polarization center is introduced. The new coordinates are introduced using a point canonical transform leading to a Hermitian Hamiltonian, with properly normalized wavefunctions, and with a Jacobian that is evaluated in closed form. All subsequent approximations to the states are manifestly translation invariant. For the ground state the energy of the recoil terms to leading order depend on the coupling constant g as g −4. The intrinsic part of the Hamiltonian determines the energy terms of order g 4 and g 0. An adiabatic canonical transformation is used to calculate all terms through order g −4. The coefficients depend on the Green's function for the electron in a static potential well. We determine the first three terms in the inverse coupling constant expansion of the effective mass.