We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying $U(1)$ gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyze the arguments of M. Peshkin and H. J. Lipkin [Phys. Rev. Lett. 74, 2847 (1995)] in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect.

• Received 14 October 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.070405