  A canonical quantization procedure is applied to the interaction of elastic
waves --phonons-- with infinitely long dislocations that can oscillate about an
equilibrium, straight line, configuration. The interaction is implemented
through the well-known Peach-Koehler force. For small dislocation excursions
away from the equilibrium position, the quantum theory can be solved to all
orders in the coupling constant. We study in detail the quantum excitations of
the dislocation line, and its interactions with phonons. The consequences for
the drag on a dislocation caused by the phonon wind are pointed out. We compute
the cross-section for phonons incident on the dislocation lines for an
arbitrary angle of incidence. The consequences for thermal transport are
explored, and we compare our results, involving a dynamic dislocation, with
those of Klemens and Carruthers, involving a static dislocation. In our case,
the relaxation time is inversely proportional to frequency, rather than
directly proportional to frequency. As a consequence, the thermal transport
anisotropy generated on a material by the presence of a highly-oriented array
of dislocations is considerably more sensitive to the frequency of each
propagating mode, and therefore, to the temperature of the material.
