  The "canonical" variables of the Kosterlitz-Thouless theory--fields
$\Phi_0({\bf r})$ and $\phi({\bf r})$, 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 $\Phi_0$ and $\phi$, and (ii) non-physical contribution of small vortex
pairs to long-range phase correlations. We resolve the paradoxes by explicitly
relating $\Phi_0$ and $\phi$ to canonical vortex-pair and phonon variables.
