Rotor winding-sector path integral
= Rotor winding-sector path integral
{title2=$\phi(\beta)-\phi(0)=2\pi m$}
The thermal rotor <path integral> traces paths closed modulo $2\pi$. Lift them to the line and sum endpoints differing by $2\pi m$. In inverse-energy time $0<\tau<\beta$, the kinetic exponent is $I\int\dot\phi^2d\tau/(2\hbar^2)$. Integer $m$ counts trajectory windings, not angular-momentum eigenstates.