The “canonical” variables of the Kosterlitz-Thouless theory—fields Φ0(r) and φ(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, canonical variables. The latter fact explains paradoxes of (i) absence of interaction between Φ0 and φ, and (ii) nonphysical contribution of small vortex pairs to long-range phase correlations. We resolve the paradoxes by explicitly relating Φ0 and φ to canonical vortex-pair and phonon variables.
Physics Review B