Vortex-Phonon Interaction in the Kosterlitz-Thouless Theory

The “canonical” variables of the Kosterlitz-Thouless theory–fields ${\mathrm{\Phi }}_0(\mathbf{r})$ and $\varphi (\mathbf{r})$, generally believed to stand for vortices and phonons (or their XY equivalents, like spin waves, etc.) turn out to be neither vortices and phonons, nor, strictly speaking, {\it canonical} variables. The latter fact explains paradoxes of (i) absence of interaction between ${\mathrm{\Phi }}_0$ and $\varphi$, and (ii) non-physical contribution of small vortex pairs to long-range phase correlations. We resolve the paradoxes by explicitly relating ${\mathrm{\Phi }}_0$ and $\varphi$ to canonical vortex-pair and phonon variables.