Path integrals with a periodic constraint: Entangled strings

Abstract

Path integrals with a periodic constraint ∫θ̇ ds =Θ̄+2πn (n=integer) are studied. In particular, the path integral for a string entangled around a singular point in two dimensions is evaluated in polar coordinates. Applications are made for the entangled polymers with and without interactions, the Aharonov–Bohm effect, and the angular momentum projection of a spinning top.