  An analytic study is presented of the E-e Jahn-Teller (JT) polaron. The
Hamiltonian is mapped onto a new Hilbert space, which is isomorphic to an
eigenspace of the angular momentum operator J, belonging to a fixed eigenvalue
j of J. In this representation, the Hamiltonian decomposes into a Holstein term
and a residual JT interaction. While the ground state of the JT polaron is
shown to belong to j=1/2, the Holstein polaron is obtained for the "unphysical"
value j=0. This is the optimal form of the Hamiltonian, which can be achieved
by purely analytic means, allowing the JT and the Holstein polaron to be
treated in a unified framework. The new Hamiltonian is then subjected to a
variational treatment, yielding the dispersion relations and effective masses
for both polarons.
