= Global phase zero mode of a finite rotor chain
{title2=$E_L=L^2/(2NI)$}
The uniform phase of a smooth N-site <coupled quantum rotor chain> remains a compact coordinate rather than a zero-frequency harmonic oscillator. At fixed total angular momentum L, minimizing the quadratic kinetic energy by a uniform local momentum gives the collective inertia NI and the displayed continuum zero-mode energy. Its allowed compact quantum numbers and any coupling to nonzero-mode boundary sectors must be imposed consistently. Removing this coordinate from oscillator products avoids a spurious divergent zero-mode partition factor.
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