  The electron motion along a chain is described by a continuum version of the
Su-Schrieffer-Heeger Hamiltonian in which phonon fields and electronic
coordinates are mapped onto the time scale. The path integral formalism allows
us to derive the non local source action for the particle interacting with the
oscillators bath. The method can be applied for any value of the {\it e-ph}
coupling. The path integral dependence on the model parameters has been
analysed by computing the partition function and some thermodynamical
properties from $T= 1K$ up to room temperature. A peculiar upturn in the low
temperature {\it heat capacity over temperature} ratio (pointing to a glassy
like behavior) has been ascribed to the time dependent electronic hopping along
the chain.
