Vortex-Phonon Interaction in the Kosterlitz-Thouless Theory

The "canonical" variables of the Kosterlitz-Thouless theory--fields $Φ_0({\bf r})$ and $ϕ({\bf r})$, 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 $Φ_0$ and $ϕ$, and (ii) non-physical contribution of small vortex pairs to long-range phase correlations. We resolve the paradoxes by explicitly relating $Φ_0$ and $ϕ$ to canonical vortex-pair and phonon variables.

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