Rotor return-kernel fluctuation prefactor
= Rotor return-kernel fluctuation prefactor
{title2=$Z_0=\sqrt{I/(2\pi\hbar^2\beta)}$}
Writing $\phi=\phi_0+2\pi m\tau/\beta+\eta$ with endpoint-fixed $\eta$ separates winding action and Gaussian fluctuations. The latter give the free return kernel on the lifted line, $Z_0=\sqrt{I/(2\pi\hbar^2\beta)}$. The starting-angle integral supplies $2\pi$. Zero winding is not the same as the zero-momentum ground-state sector.