  I propose a path integral description of the Su-Schrieffer-Heeger
Hamiltonian, both in one and two dimensions, after mapping the real space model
onto the time scale. While the lattice degrees of freedom are classical
functions of time and are integrated out exactly, the electron particle paths
are treated quantum mechanically. The method accounts for the variable range of
the electronic hopping processes. The free energy of the system and its
temperature derivatives are computed by summing at any $T$ over the ensemble of
relevant particle paths which mainly contribute to the total partition
function. In the low $T$ regime, the {\it heat capacity over T} ratio shows un
upturn peculiar to a glass-like behavior. This feature is more sizeable in the
square lattice than in the linear chain as the overall hopping potential
contribution to the total action is larger in higher dimensionality. The
effects of the electron-phonon anharmonic interactions on the phonon subsystem
are studied by the path integral cumulant expansion method.
