Path integrals with topological constraints: Aharonov-Bohm effect and polymer entanglements

Abstract

For Wiener- and Feynman integrals over paths with certain topological properties we compare various methods for explicit calculation. This leads to a one-to-one correspondence between the Aharonov-Bohm effect and a certain polymer entanglement problem. We briefly comment on two generalizations of the Aharonov-Bohm effect. First, we consider this effect due to a closed magnetic flux loop of arbitrary shape; next, we consider the combined effect due to a gas of microscopic magnetic flux loops.